Allan Marshall, 30, died in March 2015 at HMP Edinburgh after being restrained.

A Crown Office review seen by the BBC found that the police did not carry out a proper investigation and that if they had more officers would have been prosecuted.

The unpublished review said that the police should have obtained independent expert advice.

But the Crown Office also granted lifelong immunity from prosecution to the prison officers when they gave evidence at a fatal accident inquiry.

Mr Marshall had been on remand for 30 days before his next court appearance on charges of breach of the peace. He was put in the jail’s segregation unit on 24 March after officers said he became agitated. CCTV shows him being dragged into a corridor. He died four days later – the cause of death being a brain injury due to cardiac arrest.

Around 17 officers were involved at different times in restraining him. Some used their feet, which is not a normal technique. One officer admitted to stamping on Mr Marshall.

The Crown Office said it would have made a different decision had it known all the facts.

Police Scotland has since apologised in person to Mr Marshall’s relatives.

A spokesperson said: “We have received instruction from the lord advocate to investigate possible corporate responsibility by the Scottish Prison Service (SPS).

“We are not able to comment further at this time due to the live nature of this investigation.”

Teresa Medhurst, chief executive of the SPS, said: “Any death in custody is one that is felt by everyone, but in particular by the family.

“And obviously our thoughts go out to Mr Marshall’s and family. But currently this is a matter of a live investigation. So it would be inappropriate for me to make any comment at this time.”