The Royal Military Police is investigating an allegation that British special forces killed unarmed Afghan civilians, the BBC understands.
The BBC has spoken to one man who says four members of his family were killed in a night raid involving the SAS in 2011.
The Sunday Times has also reported other allegations of unlawful killing by British special forces.
An investigation into British troops' conduct in Afghanistan began in 2015.
In 2016, the Ministry of Defence said about 600 complaints against British forces in Afghanistan had been made, relating to a period between 2005 and 2013.
The MoD says 90% of those have already been dismissed, with fewer than 10% still the subject of investigation by the Royal Military Police under Operation Northmoor.
'Wall of secrecy'
One man says members of his family were killed in an SAS night raid.
The man, who did not want to be named, told the BBC he was held, blindfolded, in a room overnight.
"Early morning, they came and opened my eyes and said to me that I should not go out until they left the area. When the helicopters left the area we came out of the room.
"As soon as I came out of the room I saw that they had shot my father, two brothers and cousin."
The BBC has been told the raid did involve special forces and is now being investigated.
A former British Army intelligence officer, Chris Green, who served in Afghanistan, said he had been blocked when he tried to look into allegations of abuses by special forces officers.
"British forces, and the troops that I worked with, worked under very very strict rules of engagement and it seemed to me that special forces did not have to apply the same rules in quite the same way," he said.
"My overview of their accountability was - I didn't see any.
"When I sought information from them, this wall of secrecy was put in front of me and I could see no good reason why the information I was asking for was denied from me and nor could they give me a good reason for denying me that information."
'No witch hunts'
Labour leader Jeremy Corbyn and the former director of public prosecutions, Lord Macdonald, are among those who have called for an independent inquiry into the claims.
"Our armed forces have a reputation for decency and bravery," said Mr Corbyn.
"If we do not act on such shocking allegations we risk undermining that reputation, our security at home and the safety of those serving in the armed forces abroad."
The former head of the army, General Lord Richard Dannatt, said people shouldn't jump to conclusions.
"No witch hunts, but no cover ups," he said.
"If there is evidence of wrongdoing, it should be investigated, but we should be very, very careful of throwing mud at our very special, special forces."
Allegations of widespread abuse in Iraq have already been mostly discredited and that investigation is now closed.