The servicemen, three from the Grenadier Guards and two from the Royal Military Police, died when the officer turned his gun on them at a checkpoint in Nad-e-Ali in Helmand Province yesterday.
Another six British soldiers and two Afghan policemen were wounded in the shooting, which sent shockwaves through the coalition mission in Afghanistan.
Police in Helmand said the attacker attended a police academy in Kandahar, southern Afghanistan, and had been working as an officer in the Nad-e-Ali area for three years. He was on the roof of the checkpoint when he opened fire on the British soldiers. The UK military said every effort was being put into hunting down the killer.
Tribal elders in Helmand confirmed the attacker was a member of the Taliban called Gulbuddin, who had worked in two areas under different police commanders, ITV News reported. A Taliban spokesman told ITV News: "We want to sow mistrust between the Afghan National Police and foreign forces."
Prime Minister Gordon Brown told the House of Commons that the Taliban had claimed responsibility for the killings.
Top British, US and Afghan commanders expressed deep regret for the incident, and pledged that it would be fully investigated.
Brigadier General Mirwais Noorzai, deputy regional commander of police, said Afghan officials were committed to uncovering the truth about what happened.
He told a press conference in Helmand's provincial capital, Lashkar Gah: "I have imparted our sympathy and regret to the families of the soldiers killed."
Sitting alongside him, Major General Nick Carter, the British commander of Nato troops in southern Afghanistan, stressed that it was a joint investigation between foreign forces and the Afghan authorities.
"This absolutely demonstrates the top-level commitment of the Afghan government into coming to terms and finding out what took place in this incident and learning the appropriate lessons from it," he said.
The British servicemen were living and working at the checkpoint as part of a team mentoring Afghan National Police (ANP) officers.
The Afghan policeman apparently fired without warning before anyone could respond, then fled the scene.
Sources named the attacker as a man called Gulbuddin and suggested he was connected to the Taliban, the BBC reported.
One of the soldiers who died was named as Matthew Telford, from the Grimsby area.
His uncle, William Ferrand, told the BBC: "It was his job and he loved doing it. Nobody wants their family to go out there but it's what he wanted to do."
Speaking after the press conference Major General Carter was asked how British troops will be able to trust the Afghan police in future.
He said: "The first point I would make is that we have to trust the uniform of the Afghan police.
"The second point I would make is that we will get better at this.
"We will make it perfectly possible for us absolutely to understand who we are working with because we will train them, and we will make sure that they are capable of doing the job in the way that they need to do the job."
The killings took the UK death toll in Afghanistan since the conflict began in 2001 to 229, and made 2009 the bloodiest year for the Armed Forces since the Falklands War.
General Stanley McChrystal, the commander of Nato forces in Afghanistan, said he had received assurances from Afghan interior minister Haneef Atmar that the incident would be "fully and transparently investigated".
"We will not let this event deter our resolve to building a partnership with the Afghan national security forces to provide for Afghanistan's future," he said.
"There is a deep sense of loss as I know many others feel and our heartfelt condolences go out to the family and friends of our fellow soldiers."
Mr Brown promised to press on with the strategy of training the Afghan security forces.
He told the Commons: "It appears that they were targeted because they were engaged in what our enemies fear most - they were mentoring and strengthening Afghan forces to make Afghanistan more secure.
"While we step up and strengthen our security wherever we can, we will not stop doing what the Afghan Taliban fear most. The sacrifice of our military is great and our resolve must match it."
Tory leader David Cameron said it was a "horrific" incident which underlined the importance of "cleaning up" the Afghan police.
"Clearly the attack raises questions about the infiltration of the Afghan police by criminals, by drug dealers, by militants," he said.
Defence Secretary Bob Ainsworth emphasised the need for Britain to show "resolve" in supporting the Afghan mission.
"I was extremely saddened to hear of the deaths of these courageous soldiers. My very deepest condolences go out to their families, friends and colleagues as they come to terms with the loss of these outstanding men," he said.
"It continues to be a difficult year in Afghanistan for our brave people who are operating within the most challenging area of the country."
Meanwhile, the Stop The War Coalition said the five soldiers were "yet more victims of an unwinnable war".
An official said: "The truth is, they are dying for no other purpose than to save the reputation of politicians like Gordon Brown, who slavishly follow the dictates of US foreign policy, even when it's obvious that the world's second poorest country is no threat whatever to British interests.
"The blood of these five soldiers is on the hands of Gordon Brown. How many more British soldiers and Afghan civilians will die before he is forced to accept the inevitable and bring all the troops home?"
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