The allegations that SAS troops killed detainees in Afghanistan will not be “buried” and will be “investigated fully” if the new evidence is handed over by the BBC, a defence minister has said.

Responding to an urgent question in the Commons on new allegations concerning British Special Forces in Afghanistan, James Heappey said the Ministry of Defence (MoD) would not “rule out” any kind of investigation into the claims.

Labour argued an independent investigation into the allegations would “secure justice for any of those affected” and, above all, would “protect the reputation of our British Special Forces”.

According to BBC Panorama, British Special Forces soldiers allegedly killed detainees and unarmed men in suspicious circumstances during counterinsurgency operations in Afghanistan.

The Panorama investigation reportedly uncovered 54 suspicious killings carried out by one British SAS unit on a six-month tour of Afghanistan in 2010/11.

Mr Heappey said it was his understanding that the “allegedly criminal events referred to in the Panorama programme have been fully investigated by the service police” but stressed that the MoD remained “fully committed to any further reviews from investigations where new evidence or reason to do so is presented”.

He told the Commons that the Royal Military Police (RMP) and BBC were in discussions about Panorama handing over any new evidence.

He said: “A decision to investigate the allegations of criminality is for the service police. They provide an independent and impartial investigative capability, free from improper interference.

“Earlier this week, the Royal Military Police wrote to the production team of Panorama to request that any new evidence be provided to them … I understand that the BBC has responded to question the legal basis on which the RMP are requesting that new evidence, which makes little sense to me, but the RMP and the BBC are in discussions.”

Shadow defence secretary John Healey said similar allegations against Australian special forces had been subject to an independent investigation, asking: “Will the Government now do the same?

“To investigate these claims and any cover-ups in the chain of command, to secure justice for any of those affected, and above all to protect the reputation of our British Special Forces?”

The defence minister said the allegations “won’t be buried”, adding: “That does no service to our armed forces whatsoever. They will be investigated fully if the new evidence is handed over.”

He added: “The Secretary of State was very clear when I spoke to him earlier in the week on this matter, that he is not ruling out any type of public inquiry or review.

“If it is clear that there are failings that need to be looked at, the MoD wants this to be as transparent as possible so that everybody can have confidence in the service justice system and the reputation of our armed forces can remain untarnished.”

Independent MP and former Labour leader Jeremy Corbyn asked the minister if he thought it was “appropriate” for the RMP to investigate the allegations and whether “it’s time for special forces to be brought under the same democratic accountability as the rest of the armed services”.

Mr Heappey replied: “I have every confidence in the independence of the Royal Military Police as an independent police force, free of political influence or influence from the chain of command, just like I have confidence that all other police forces are proudly operational, independent.

“And no, I don’t think that the special forces should be moved into a position of more overt democratic oversight. And the reason for that is the work that they do is right at the extreme end of the threat envelope, the risk to life and limb is profound.

“What they do in defence of our nation’s interests is extraordinary. And if we were to compromise that even in the slightest, our nation would be at a disadvantage and brave people would be in severe peril.”