Cpl Nicholas Webster-Smith was killed along with four other soldiers
The five British soldiers killed in an attack by an Afghan police officer have been named by the Ministry of Defence.
They were Warrant Officer Darren Chant, Sgt Matthew Telford, Guardsman James Major, Acting Cpl Steven Boote and Cpl Nicholas Webster-Smith.
A "rogue" Afghan policeman has been blamed by the UK military, but PM Gordon Brown has said the Taliban could have infiltrated the police.
The dead soldiers had been mentoring Afghan police in Helmand province.
WO1 Chant, Sgt Telford and Guardsman Major were from the Grenadier Guards, while Acting Cpl Boote and Cpl Webster-Smith were from the Royal Military Police.
They had been working and living in a compound at a national police checkpoint in the Nad Ali district for the last two weeks.
Six British servicemen and two Afghan National Police (ANP) officers were also injured in Tuesday's attack.
Taliban link probed
"While we are assembling evidence, the Taliban have claimed responsibility for this incident," Mr Brown told MPs in the Commons on Wednesday.
"It may be that the Taliban have used an Afghan police member or they have infiltrated the Afghan police force and that is what we've got to look at," he said.
Sgt Matthew Telford joined the Army when he was 16
However, BBC Kabul correspondent Ian Pannell later said the Taliban had not admitted carrying out the attack.
Mr Brown said training of Afghan police remained an "essential element" of the strategy in Afghanistan and would not be stopped because it was "what the Taliban fears most".
"We will have to increase the number of police but it's clear we will have to increase the quality of police as well," he told the Commons.
"I would not want to draw conclusions about all the Afghan police from one single incident," he added.
William Ferrand, the uncle of Sgt Telford, said his nephew had "absolutely loved" his job training Afghan forces.
He added: "Everybody knows what a wonderful lad he was. It has devastated all of us."
Sgt Telford, of Grimsby, leaves a wife, Kerry, and two sons aged nine and four.
Paul Thundercliffe taught Guardsman Major at the Lindsey School in Cleethorpes, Lincolnshire.
"He had a cheeky smile and he always wanted to make you understand where he was coming from," he told the BBC.
"He was very forthright and as he went through the school he just wanted to get better and better at everything that he did."
A total of 92 UK servicemen have now been killed this year, the highest annual figure since the Falklands War in 1982.
A UK military spokesman said: "One individual Afghan National Policeman, possibly in conjunction with another, went rogue.
BBC defence correspondent
Training the Afghan police as well as the Afghan army is key to Nato's plans in Afghanistan, so they can ultimately take over security across the country, allowing British and American forces and their allies to gradually leave.
However, recruiting and training the police and ensuring their loyalty to the Afghan government has long been extremely difficult. In Helmand especially, the police are proving less reliable - as well as more corrupt - than the Afghan Army.
The Afghan police are relatively badly paid - earning rather less than a Taliban fighter - and are said to earn extra cash from taking bribes from ordinary Afghans at official or often unofficial checkpoints.
"His motives and whereabouts are unknown at this time. Every effort is now being put into hunting down those responsible for this attack."
The officer was on the roof of the checkpoint when he opened fire on the soldiers, police in Helmand said.
Ian Pannell said sources had indicated the attacker was a police officer called Gulbuddin who had fled the scene after the shooting.
It appears he could have been involved in a dispute with his commander, but tribal sources have pointed to a link with the Taliban, our correspondent said.
Lt Col David Wakefield, spokesman for Task Force Helmand, said the attack had not been a result of any breakdown or fight between British and Afghan forces.
The prime minister said the latest deaths were a "terrible loss".
He said: "My thoughts, condolences and sympathies go to their families, loved ones and colleagues. I know that the whole country too will mourn their loss."
Tory leader David Cameron said: "I pay tribute, as will the whole country, to their professionalism and their courage, and send my condolences to their families and their friends."
Gen Stanley McChrystal, commander of the International Security Assistance Force, said he had spoken to the Afghan Minister of Interior, Hanif Atmar, who shared his regret for the incident.
"He gave me his assurance that this incident will be fully and transparently investigated," he said.
"We will not let this event deter our resolve to build a partnership with the Afghan National Security Forces to provide for Afghanistan's future."
A former commander of British forces in Afghanistan, Col Richard Kemp, said the shootings were a very worrying development.
He said: "It will undermine trust, certainly in the short term, until we establish exactly what happened. And it wouldn't at all surprise me now if there aren't a lot of soldiers, British soldiers in Afghanistan, with their fingers very firmly on the trigger when they're around Afghan police and military."
The British Military Police have launched an investigation. The local ANP chief and the Afghan national director of security have also begun investigating at the scene.
There were similar incidents involving the deaths of two US personnel last month and two more in 2008.
The British casualties were evacuated to the field hospital at Camp Bastion in Helmand by medical emergency response teams using Chinook and US Black Hawk helicopters.
The deaths take the number of UK troops killed in Afghanistan since 2001 to 229.
This is the worst single incident in Helmand since 10 July, when five soldiers from 2 Rifles were killed by bombs near the town of Sangin.