The defence ministry said the soldiers had been shot dead on Sunday at a checkpoint in Nahr-e-Saraj in the southwestern Helmand province, where they were meeting local elders.
"I was saddened to hear of this cowardly act by a man wearing an Afghan uniform, which has taken the lives of three brave British soldiers," minister Philip Hammond said.
"Every day, tens of thousands of coalition forces, including UK personnel, live and work successfully with their Afghan counterparts to build an Afghan police force and Army which can take the lead for their own security by the end of 2014," he added.
"That process will continue, and though deeply tragic, yesterday's incident and attacks like it will not derail the mission or distract us from the task in hand."
Prime Minister David Cameron said he was "deeply saddened" by the killings.
"My heart goes out to their families," he said. "These brave soldiers were demonstrating great courage to help prevent Afghanistan once again become a haven for international terrorists."
NATO's International Security Assistance Force (ISAF) had first reported the deaths of three soldiers on Sunday, without revealing the nationality of the victims in keeping with its usual policy.
An ISAF spokesman said that the gunman was wounded and detained after the attack, which happened around 5:00 pm (1230 GMT), and was now under investigation.
ISAF was investigating whether or not the attacker was a police officer, he added.
The British defence ministry said the soldiers, who were serving with an Afghan police advisory team, had gone to the Kamparack Pul checkpoint for a "shura" -- a meeting with Afghan elders.
The soldiers' families have been informed.
The deaths take the toll this year in "green-on-blue" killings -- in which Afghan forces turn their weapons against their Western allies -- to at least 26, in a total of 18 such incidents.
The latest attack comes nearly two weeks after three men in Afghan police uniforms killed a soldier with the US-led ISAF force, also in the south.
An increasing number of Afghan troops have turned their weapons against NATO soldiers who are helping Kabul fight a decade-long insurgency by hardline Taliban Islamists.
Some of the assaults are claimed by the Taliban, who say they have infiltrated the ranks of Afghan security forces, but many are attributed to cultural differences and antagonism between the allied forces.
NATO has around 130,000 soldiers fighting alongside some 350,000 Afghan security personnel against the Taliban-led insurgency, but they are due to pull out of the country in 2014.
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