The British prime minster held an urgent meeting with his advisers shortly after a video purporting to show the beheading of British hostage David Haines was released.
TV footage showed David Cameron getting out of his car and going into Downing Street just after midnight.
Cameron will also chair a meeting of the government's emergency Cobra committee this morning to discuss the UK's response to the Islamic State (IS) group, which said it killed Haines in response to London's promise to arm Iraqi Kurdish troops to fight its militants.
Cameron has vowed to do everything in the government's power to crackdown on the killers.
Downing Street has quoted Cameron as condemning the killing as "an act of pure evil."
The United States pledged to work with UK and other regional and world countries to destroy IS.
IS released late last night a video purporting to show the beheading of Haines, a British aid worker, kidnapped by IS militants in Syria last year.
While Cameron confirmed Haines' death, the British Foreign Office had said earlier that it was “working urgently to verify the video.''
Haines is the third Westerner beheaded in recent weeks by IS, which has seized wide swaths of territory in Syria and Iraq.
The group killed a US journalist, James Foley, last month, before it beheaded another journalist, Steven Sotloff, earlier this month.
Cameron said the family of Haines had shown extraordinary courage.
“We will do everything in our power to hunt down these murderers and ensure they face justice, however long it takes."
Haines' family said in a statement, "He was and is loved by all his family and will be missed terribly."
Haines was taken hostage in the village of Atmeh, in the Idlib province of Syria, in March 2013.
In the video, a second British hostage is threatened with execution.
It contains the words of the IS masked man saying: "This British man has to pay the price for your promise, Cameron, to arm the Peshmerga (the Iraqi Kurdish armed forces) against the Islamic State."
The leader of the British opposition called Haines’ killing "barbaric."
US President Barak Obama said his country strongly condemned “the barbaric murder of UK citizen.”
“The United States stands shoulder to shoulder tonight with our close friend and ally in grief and resolve,” he said.
Obama confirmed: “We will work with the United Kingdom and a broad coalition of nations from the region and around the world to bring the perpetrators of this outrageous act to justice, and to degrade and destroy this threat to the people of our countries, the region and the world.”
"I am sickened at the disgusting, barbaric killing of David Haines," Ed Miliband, leader of the Labour Party, said in a statement.
"He was somebody whose only purpose was to help innocent people, themselves victims of conflict," he added
"That ISIL would choose to kill him says everything about their warped logic and murderous ways."
In response to the video posted by IS the First Minister of Scotland, Alex Salmond said: "The release of the video has demonstrated a degree of brutality which defies description.
“It should be remembered that Mr Haines was in the region as an aid worker helping local people,” he said in a statement.