The 44-year-old aid worker, from Perth, was kidnapped in Syria in 2013. He was being held by Islamic State militants who have already killed two Americans.
The latest video also includes a threat to kill a second British hostage.
The PM vowed to do everything possible to find the killers. Mr Haines's family said he would be "missed terribly".
'Despicable and appalling'In a statement released by the Foreign Office, Mike Haines said his brother, a father of two, "was and is loved by all his family".
"David was most alive and enthusiastic in his humanitarian roles. His joy and anticipation for the work he went to do in Syria is for myself and family the most important element of this whole sad affair," he said.
The latest video also includes a threat to kill a second British hostage.
The PM vowed to do everything possible to find the killers. Mr Haines's family said he would be "missed terribly".
'Despicable and appalling'In a statement released by the Foreign Office, Mike Haines said his brother, a father of two, "was and is loved by all his family".
"David was most alive and enthusiastic in his humanitarian roles. His joy and anticipation for the work he went to do in Syria is for myself and family the most important element of this whole sad affair," he said.
Mr Cameron, who is due to chair an emergency Cobra committee meeting later, said the murder of an innocent aid worker was "despicable and appalling".
"It is an act of pure evil. My heart goes out to the family of David Haines who have shown extraordinary courage and fortitude throughout this ordeal.
"We will do everything in our power to hunt down these murderers and ensure they face justice, however long it takes," the prime minister added.
'Grief and resolve'The Foreign Office is working to verify the video, which was released on Saturday night. It begins with a clip of Mr Cameron and then features a man who appears to be Mr Haines dressed in orange overalls, kneeling in front of a masked man holding a knife.
The victim says: "My name is David Cawthorne Haines. I would like to declare that I hold you, David Cameron, entirely responsible for my execution."
He says Mr Cameron had entered into a coalition with the US against the Islamic State "just as your predecessor Tony Blair did".
"Unfortunately it is we the British public that in the end will pay the price for our parliament's selfish decisions," he said.
The militant, who appears to have a British accent, is then recorded as saying: "This British man has to the pay the price for your promise, Cameron, to arm the Peshmerga against the Islamic State."
"It is an act of pure evil. My heart goes out to the family of David Haines who have shown extraordinary courage and fortitude throughout this ordeal.
"We will do everything in our power to hunt down these murderers and ensure they face justice, however long it takes," the prime minister added.
'Grief and resolve'The Foreign Office is working to verify the video, which was released on Saturday night. It begins with a clip of Mr Cameron and then features a man who appears to be Mr Haines dressed in orange overalls, kneeling in front of a masked man holding a knife.
The victim says: "My name is David Cawthorne Haines. I would like to declare that I hold you, David Cameron, entirely responsible for my execution."
He says Mr Cameron had entered into a coalition with the US against the Islamic State "just as your predecessor Tony Blair did".
"Unfortunately it is we the British public that in the end will pay the price for our parliament's selfish decisions," he said.
The militant, who appears to have a British accent, is then recorded as saying: "This British man has to the pay the price for your promise, Cameron, to arm the Peshmerga against the Islamic State."
The UK has donated heavy machine guns and ammunition to authorities in Iraq to help fight IS militants, the Ministry of Defence previously said.
Kurdish forces, known as the Peshmerga, have been involved in heavy fighting with IS.
US President Barack Obama said "our hearts go out to the family of Mr Haines and to the people of the United Kingdom".
In a statement he said the US would work with the UK and a "broad coalition of nations" to "bring the perpetrators of this outrageous act to justice".
"The United States stands shoulder to shoulder tonight with our close friend and ally in grief and resolve," he added.
Scottish First Minister Alex Salmond said the release of the video "demonstrated a degree of brutality which defies description".
Labour leader Ed Miliband said he was "sickened at the disgusting, barbaric killing" of Mr Haines.
Kurdish forces, known as the Peshmerga, have been involved in heavy fighting with IS.
US President Barack Obama said "our hearts go out to the family of Mr Haines and to the people of the United Kingdom".
In a statement he said the US would work with the UK and a "broad coalition of nations" to "bring the perpetrators of this outrageous act to justice".
"The United States stands shoulder to shoulder tonight with our close friend and ally in grief and resolve," he added.
Scottish First Minister Alex Salmond said the release of the video "demonstrated a degree of brutality which defies description".
Labour leader Ed Miliband said he was "sickened at the disgusting, barbaric killing" of Mr Haines.
Mr Haines was taken hostage in the village of Atmeh, in the Idlib province of Syria, in March 2013.
He had been helping French agency Acted deliver humanitarian aid, having previously helped local people in Libya and South Sudan.
The release of the video came hours after his family had made a direct appeal to IS to contact them.
IS - also known as Isis or Isil - has seized large swathes of territory in Iraq and Syria and declared a new caliphate - or Islamic state.
Militants from the extremist group have killed two US hostages in recent weeks, posting video evidence on the internet.
They threatened to kill Mr Haines during a video posted online showing the killing of US journalist Steven Sotloff earlier this month.
The extremist group also killed fellow US journalist, James Foley, last month.
He had been helping French agency Acted deliver humanitarian aid, having previously helped local people in Libya and South Sudan.
The release of the video came hours after his family had made a direct appeal to IS to contact them.
IS - also known as Isis or Isil - has seized large swathes of territory in Iraq and Syria and declared a new caliphate - or Islamic state.
Militants from the extremist group have killed two US hostages in recent weeks, posting video evidence on the internet.
They threatened to kill Mr Haines during a video posted online showing the killing of US journalist Steven Sotloff earlier this month.
The extremist group also killed fellow US journalist, James Foley, last month.
[h=3]RTRENDING TRIBUTE PAID BY MR HAINES'S BROTHER[/h]Mr Haines's brother, Mike, paid tribute to him last night, saying: 'My name is Mike Haines, I am brother to David Haines, who was recently murdered in cold blood.
'David was like so very many of us, just another bloke. Born in 1970 to parents who loved us both, our childhood was centred around our family. Holidays in caravans and tents, days away as a family which we remember fondly.
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Proud father: David Haines was an enthusiastic humanitarian, his brother has said
'David and I were brought up to know right from wrong, although we might not with the innocence of youth have always chosen right.
'David was a good brother, there when I needed him and absent when I didn't. I hope that he felt the same way about me.
'He was, in the right mood, the life and soul of the party and on other times the most stubborn irritating pain in the ass. He would probably say the same about me.
'After leaving school he worked with the Royal Mail before joining the RAF as an aircraft engineer.
'He married his childhood sweetheart Louise and in the due process of time had a wee lass Bethany. He was – and no doubt wherever he is – exceptionally proud of Bethany.
'David served with the UN in the Balkans, helping people in real need. There are many accolades from people in that region that David helped. He helped whoever needed help, regardless of race, creed or religion.
'During this time David began to decide that humanitarian work was the field he wanted to work in.
'David left the RAF and was employed by Scotrail. As with every job, David entered into it with enthusiasm. David met and married his second wife Dragana and they have a four year old daughter Athea.
'David was most alive and enthusiastic in his humanitarian roles. His joy and anticipation for the work he went to do in Syria is for myself and family the most important element of this whole sad affair. He was and is loved by all his family and will be missed terribly.'
'David was like so very many of us, just another bloke. Born in 1970 to parents who loved us both, our childhood was centred around our family. Holidays in caravans and tents, days away as a family which we remember fondly.
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Proud father: David Haines was an enthusiastic humanitarian, his brother has said
'David and I were brought up to know right from wrong, although we might not with the innocence of youth have always chosen right.
'David was a good brother, there when I needed him and absent when I didn't. I hope that he felt the same way about me.
'He was, in the right mood, the life and soul of the party and on other times the most stubborn irritating pain in the ass. He would probably say the same about me.
'After leaving school he worked with the Royal Mail before joining the RAF as an aircraft engineer.
'He married his childhood sweetheart Louise and in the due process of time had a wee lass Bethany. He was – and no doubt wherever he is – exceptionally proud of Bethany.
'David served with the UN in the Balkans, helping people in real need. There are many accolades from people in that region that David helped. He helped whoever needed help, regardless of race, creed or religion.
'During this time David began to decide that humanitarian work was the field he wanted to work in.
'David left the RAF and was employed by Scotrail. As with every job, David entered into it with enthusiasm. David met and married his second wife Dragana and they have a four year old daughter Athea.
'David was most alive and enthusiastic in his humanitarian roles. His joy and anticipation for the work he went to do in Syria is for myself and family the most important element of this whole sad affair. He was and is loved by all his family and will be missed terribly.'
n the video, titled A Message to the Allies of America, the extremists also threatened to execute another Briton who is paraded before the camera.
The video began with recent news footage of Prime Minister David Cameron discussing Britain's foreign policy towards Islamic State.
It then cut to the man kneeling in an orange jumpsuit in the desert. Reciting what appeared to be a prepared script, he said: 'My name is David Cawthorne Haines. I would like to declare that I hold you David Cameron entirely responsible for my execution.
'You entered voluntarily into a coalition with the United States against the Islamic State, just as your predecessor Tony Blair did, following a trend amongst our British Prime Minsters who can't find the courage to say no to the Americans.
'Unfortunately it is we the British public that in the end will pay the price for our Parliament's selfish decisions.'
The Islamic State militant, who has a British accent, then said: 'This British man has to the pay the price for your promise, Cameron, to arm the Peshmerga against the Islamic State.
'Ironically he has spent a decade of his life serving under the same Royal Air Force that is responsible for delivering those arms.
'Your evil alliance with America which continues to strike the Muslims of Iraq and most recently bombed the Haditha Dam will only accelerate your destruction, and playing the role of the obedient lapdog, Cameron, will only drag you and your people into another bloody and unwinnable war.'
The footage then showed what is believed to be the body of Mr Haines.
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Family man: The 44-year-old has a teenage daughter in Scotland and a four-year-old daughter in Croatia
.
The video was released hours after Mr Haines' family made a direct plea to his captors to contact them. His second wife, Dragana Prodanovic Haines (pictured with him), previously said she cried for her husband daily
.
The video began with recent news footage of Prime Minister David Cameron discussing Britain's foreign policy towards Islamic State.
It then cut to the man kneeling in an orange jumpsuit in the desert. Reciting what appeared to be a prepared script, he said: 'My name is David Cawthorne Haines. I would like to declare that I hold you David Cameron entirely responsible for my execution.
'You entered voluntarily into a coalition with the United States against the Islamic State, just as your predecessor Tony Blair did, following a trend amongst our British Prime Minsters who can't find the courage to say no to the Americans.
'Unfortunately it is we the British public that in the end will pay the price for our Parliament's selfish decisions.'
The Islamic State militant, who has a British accent, then said: 'This British man has to the pay the price for your promise, Cameron, to arm the Peshmerga against the Islamic State.
'Ironically he has spent a decade of his life serving under the same Royal Air Force that is responsible for delivering those arms.
'Your evil alliance with America which continues to strike the Muslims of Iraq and most recently bombed the Haditha Dam will only accelerate your destruction, and playing the role of the obedient lapdog, Cameron, will only drag you and your people into another bloody and unwinnable war.'
The footage then showed what is believed to be the body of Mr Haines.
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Family man: The 44-year-old has a teenage daughter in Scotland and a four-year-old daughter in Croatia
.
The video was released hours after Mr Haines' family made a direct plea to his captors to contact them. His second wife, Dragana Prodanovic Haines (pictured with him), previously said she cried for her husband daily
.
[h=3]LIFE OF FATHER-OF-TWO FROM SCOTLAND WHO DEDICATED HIS LIFE TO PROMOTING PEACE IN PLACES OF VIOLENT CONFLICT[/h]The British father-of-two murdered at the hands of Islamic State fanatics spent his career as an aid worker helping to protect innocent civilians across the Third World.
For more than two decades, David Cawthorne Haines travelled with aid agencies through Syria, Libya, the former Yugoslavia and South Sudan.
He dedicated his life to promoting peace in places of violent conflict and oversaw projects to save civilians from land mines.
The 44-year-old was described as a hero by his family, who were inspired by him to travel the world on further aid missions.
He had a teenage daughter in Scotland from a previous marriage with his first wife, and a four-year-old daughter, Athea, in Croatia from his second wife.
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Mr Haines was born in Holderness in East Yorkshire and brought up in Perth by his parents Herbert, 77, and Mary, 79, who now live in Ayr.
He studied at Perth Academy before joining the military aged 17.
According to his online CV he spent 11 years in the military, holding 'various positions covering security and threat assessments in a number of different countries' between 1988 and 1999.
It did not specify with which armed forces he served, although the Islamic State video claimed he had been in the Royal Air Force.
Despite getting married to his first wife when he was 22 – and having his first daughter five years later – Mr Haines was determined to continue working across the world to help civilians trapped in war-torn countries.
Between 1999 and 2004, he was at a German NGO helping to revive abandoned villages and to return refugees to their homes after the civil war in the former Yugoslavia.
The work led to swift promotion and he left a few years later to become an independent consultant, spreading his experience in dealing with security to various charities and organisations.
He worked as a consultant director for manufacturing company Astraea, based in Croatia, and went to Libya three years ago, working with Handicap International on demining programmes. The charity said Mr Haines had worked as 'a humanitarian' since 1999, helping people in the Balkans, the Middle East and Africa.
A year later, the aid worker travelled to South Sudan, where he was a security manager for Nonviolent Peaceforce, a civilian peacekeeping group.
Wanting more freedom and a shorter-term contract, Mr Haines left to join French non-governmental organisation ACTED, or the Agency for Technical Cooperation and Development, which works to support civilians affected by wars, natural disasters and economic and social crises.
Mr Haines met his wife, Dragana Prodanovic Haines, 45, when she was working as a translator. At the time, Mr Haines was helping refugees return to their homes after the Balkans war.
The couple ran a supplies business from their home near Zagreb, where friends said their relationship was 'a true love story' and they were ecstatic when she became pregnant with their daughter at the age of 41.
The couple, who married in Croatia in 2010 in a ceremony in which Mr Haines wore a kilt, were due to celebrate their fourth wedding anniversary in November.
Earlier this month, she described how she 'cries every day' for her husband, but has yet to tell their child of his capture.
He was with ACTED in Syria – whom he had been working for for just ten days - when he was kidnapped with a colleague, Italian aid worker Federico Motka, 31, in March last year by IS forces near the Atmeh refugee camp, by the Turkish border.
Mr Motka was released in May, after a ransom was paid.
Mr Haines' plight came to light at the end of a video showing the beheading of US journalist Steven Sotloff earlier this month.
He was being held by a group that included at least one of the British jihadis linked to the kidnap and killing of James Foley and Steven Sotloff, who have been nicknamed 'The Beatles'.
Reports from those with connections to the militants said Haines developed vomiting and diarrhoea.
He was also said to have been beaten so badly that his kidnappers were forced to arrange medical treatment.
For more than two decades, David Cawthorne Haines travelled with aid agencies through Syria, Libya, the former Yugoslavia and South Sudan.
He dedicated his life to promoting peace in places of violent conflict and oversaw projects to save civilians from land mines.
The 44-year-old was described as a hero by his family, who were inspired by him to travel the world on further aid missions.
He had a teenage daughter in Scotland from a previous marriage with his first wife, and a four-year-old daughter, Athea, in Croatia from his second wife.
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Mr Haines was born in Holderness in East Yorkshire and brought up in Perth by his parents Herbert, 77, and Mary, 79, who now live in Ayr.
He studied at Perth Academy before joining the military aged 17.
According to his online CV he spent 11 years in the military, holding 'various positions covering security and threat assessments in a number of different countries' between 1988 and 1999.
It did not specify with which armed forces he served, although the Islamic State video claimed he had been in the Royal Air Force.
Despite getting married to his first wife when he was 22 – and having his first daughter five years later – Mr Haines was determined to continue working across the world to help civilians trapped in war-torn countries.
Between 1999 and 2004, he was at a German NGO helping to revive abandoned villages and to return refugees to their homes after the civil war in the former Yugoslavia.
The work led to swift promotion and he left a few years later to become an independent consultant, spreading his experience in dealing with security to various charities and organisations.
He worked as a consultant director for manufacturing company Astraea, based in Croatia, and went to Libya three years ago, working with Handicap International on demining programmes. The charity said Mr Haines had worked as 'a humanitarian' since 1999, helping people in the Balkans, the Middle East and Africa.
A year later, the aid worker travelled to South Sudan, where he was a security manager for Nonviolent Peaceforce, a civilian peacekeeping group.
Wanting more freedom and a shorter-term contract, Mr Haines left to join French non-governmental organisation ACTED, or the Agency for Technical Cooperation and Development, which works to support civilians affected by wars, natural disasters and economic and social crises.
Mr Haines met his wife, Dragana Prodanovic Haines, 45, when she was working as a translator. At the time, Mr Haines was helping refugees return to their homes after the Balkans war.
The couple ran a supplies business from their home near Zagreb, where friends said their relationship was 'a true love story' and they were ecstatic when she became pregnant with their daughter at the age of 41.
The couple, who married in Croatia in 2010 in a ceremony in which Mr Haines wore a kilt, were due to celebrate their fourth wedding anniversary in November.
Earlier this month, she described how she 'cries every day' for her husband, but has yet to tell their child of his capture.
He was with ACTED in Syria – whom he had been working for for just ten days - when he was kidnapped with a colleague, Italian aid worker Federico Motka, 31, in March last year by IS forces near the Atmeh refugee camp, by the Turkish border.
Mr Motka was released in May, after a ransom was paid.
Mr Haines' plight came to light at the end of a video showing the beheading of US journalist Steven Sotloff earlier this month.
He was being held by a group that included at least one of the British jihadis linked to the kidnap and killing of James Foley and Steven Sotloff, who have been nicknamed 'The Beatles'.
Reports from those with connections to the militants said Haines developed vomiting and diarrhoea.
He was also said to have been beaten so badly that his kidnappers were forced to arrange medical treatment.
