A British army chief says the military’s reputation has been damaged by claims of illegal and “downright unacceptable” conduct, including an alleged sexual assault.

The chief of the general staff, Gen Sir Mark Carleton-Smith, emphasised to troops that any inappropriate behaviour was “downright unacceptable” in an unprecedented video message after six British army soldiers were arrested over an alleged sexual assault against a teenage female soldier.

The defence secretary, Gavin Williamson, said earlier he was “appalled” by the allegations and was launching a review of behaviour across the military.

“There is no place for these kind of actions in the military and, if true, those involved must face the full force of the law,” Williamson said. “I have commissioned a review into inappropriate behaviour in the military with a view to stamping it out.”

Although he said it was not appropriate to comment upon specific claims, Carleton-Smith said: “Over the last few days a series of exceptionally serious allegations have been made against soldiers currently serving in the British army.

“All these allegations are being taken very seriously by the military chain of command and are now under active investigation by the police, which is exactly as it should be and what I expect. Because of that, it’s not appropriate for me to comment specifically any further on them.

“But I will say this: where serious allegations are proven against members of the army, including allegations of a violent or sexual nature, it demonstrates indiscipline that is wildly at odds with the values and standards that represent the fabric of not just our army but the nation’s army, the British army.”

He added: “Not only is it downright unacceptable, it is illegal and it stands in stark contrast with everything the British army represents.”

The army had faced criticism this week when a video emerged showing soldiers using a picture of Jeremy Corbyn for target practice. The Ministry of Defence launched an investigation into the conduct of the personnel from 3rd Battalion, Parachute Regiment, who were filmed in Kabul, Afghanistan, shooting at a picture of the Labour leader.

Carleton-Smith said: “This hasn’t been a good week for the army. It has damaged our reputation, which is exceptionally hard-earned and includes the sacrifice of our friends on the battlefield.”