Farid Ahmad Farhang, a spokesman for the provincial police, claimed the British had been killed by friendly fire after a case of mistaken identity.
He said shooting had broken out after a British patrol encountered an Afghan policeman who had left his nearby checkpoint to wash before prayers. The policeman was not wearing uniform, but had his weapon with him.
The patrol mistook the policeman for a Taliban fighter and shot him dead, but another British unit on patrol nearby had thought it was under attack and fired, accidentally killing the two Britons, Mr Farhang said.
Other reports suggested that after the policeman had been shot, his comrades believed they were being attacked and fired back, intensifying the gun battle with the British patrol.
British officers were also meanwhile checking the possibility the patrol had been deliberately attacked by the policeman. A rash of so-called insider attacks where Afghan forces turn their weapons on Nato troops has sown deep distrust between the ranks of the allies.
In a separate incident, two American soldiers were shot dead in Uruzgan province on Thursday by a man believed to be a policeman.
Nine British troops have been shot dead by their Afghan comrades this year, accounting for nearly a quarter of all British deaths in Afghanistan.
A spokesman for the Ministry of Defence said the British troops had died in an "exchange of fire" along with an Afghan man believed to have been a policeman. The British patrol was not accompanied by any Afghan forces, he said.
"At this stage we do not know what initiated the exchange of gunfire and an investigation is on going," he said.
"Further details will be provided as information becomes available but at this time the situation remains unclear."
The Nato-led coalition in Kabul initially said the two Britons had been killed by the Taliban, but then said the cause was under investigation.
Inquiries into what happened on the patrol on Wednesday afternoon have been hampered because several witnesses were also wounded during the exchange and have not yet been questioned.
"There's still a very confusing situation on the ground, and we have not yet been able to interview some members of the patrol," said one military source.
Major Laurence Roche, spokesman for British forces in Helmand, said: "This is dreadful news for all of us serving in Afghanistan. Our sincere condolences go to their families, friends and colleagues at this time of grief."
The deaths provoked clashes in the House of Commons, with a Labour MP alleging the casualties had died to protect the reputations of "cowardly ministers".
Paul Flynn said: "Today we hear the dreadful news of two further deaths of British soldiers. There will be many tributes to them that will be sincere and heartfelt.
"But won't history judge their epitaph should be: they died to protect the reputation of cowardly ministers?"
Other MPs urged Mr Flynn to withdraw the remark, but the Speaker made no intervention.
Mr Flynn, member for Newport West, has repeatedly called for an early withdrawal of British troops. Last month he was kicked out of the Commons and suspended for calling the Defence Secretary, Philip Hammond, and his ministers liars.