Claims that "rogue" Special Air Service (SAS) soldiers killed unarmed Afghan civilians in cold blood and attempted to cover up the evidence should be probed in an independent inquiry, British Opposition Leader Jeremy Corbyn says.

He said there was a risk the British armed forces' reputation for decency and bravery would be undermined unless the claims in the Sunday Times were investigated.

According to the newspaper, which quoted senior military police and defence sources, there is "strong evidence" SAS personnel killed rather than captured unarmed Afghan civilians who were suspected of being Taliban insurgents during night raids on their homes.

The allegations emerged in Operation Northmoor, a Royal Military Police (RMP) investigation, the Sunday Times reported.

The Ministry of Defence (MoD) said the RMP found no evidence of criminal behaviour by British armed forces in Afghanistan to date.

In February, Defence Secretary Sir Michael Fallon announced 90 per cent of the probe's misconduct cases involving British troops who served in Afghanistan were to be dropped, amid controversy over a discredited probe into Iraq war veterans.

Commenting on the claims, Corbyn said: "The allegations of unlawful killings and war crimes in Afghanistan are extremely serious and must be fully investigated.

"Our armed forces have a reputation for decency and bravery. 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."

Corbyn said there could be no question of a cover-up and the government must establish an independent inquiry into the claims.

A Ministry of Defence spokesman said the Royal Military Police had found no evidence of criminal behaviour by the armed forces in Afghanistan but where allegations were raised it was right they were investigated.