London - Prime Minister David Cameron said on Wednesday that Britain was paying a "very high price" in Afghanistan after three soldiers were killed by a roadside bomb.
Six British soldiers have now been killed this year in Afghanistan, where British casualties have slowed over the past year.
Britain has not lost so many soldiers in one incident since six were killed by a similar blast in March last year.
The defence ministry named the men as Corporal William Thomas Savage, Fusilier Samuel Flint and Private Robert Murray Hetherington.
They received immediate medical attention at the scene of the blast in Helmand province on Tuesday and were evacuated by air to Britain's main Camp Bastion base but could not be saved, the ministry said.
The deaths take the total number of British troops killed by enemy action in Afghanistan over the 400 mark, to 401, of a total of 444 who have lost their lives in the campaign begun in October 2001.
"We have paid a very high price for the work we're doing in Afghanistan," Cameron told ITV television.
"It is important work because it's vital that country doesn't again become a haven for terrorists - terrorists that can threaten us here in the UK.
"But today our thoughts should be with the families and friends of those that have suffered."
The three soldiers' vehicle was hit on a routine patrol in the district of Nahr-e Saraj.
"Their deaths come as a great loss to all those serving in Task Force Helmand," spokesperson Major Richard Morgan said in a statement.
Withdrawal from Afghanistan
Defence Secretary Philip Hammond said he was "deeply saddened" by the news.
"It is clear from the tributes paid to them that they were exceptional men who served their country with distinction," he added.
Their families have been informed.
It is the first time since September 2012 that British troops have been killed by a roadside bomb, which have caused many of the British deaths in Afghanistan.
There was no immediate claim of responsibility but Taliban militants frequently use roadside bombs against foreign troops and their Afghan allies.
The defence ministry said that security in Helmand, a hotbed of the Taliban insurgency, was improving but that it remained a risky and dangerous environment for British troops.
Afghan police and soldiers are taking over responsibility for security, but there is growing concern over the war-torn country's prospects after 2014 when all foreign combat deployments will end.
General Richard Dannatt, the former head of the British army, was asked on Wednesday whether it was harder to justify the deaths given that British forces will soon withdraw from Afghanistan.
He told BBC radio: "It certainly makes deaths like these ones more painful as we are close to the end.
"Often those who we are fighting increase their efforts towards the end to try and play up the fact that they have driven us out or to increase their hand in bargaining at the negotiating table subsequently."