At a preliminary hearing over the public inquiry into the death of Mr Bayoh in May 2015, lawyers warned there could be “unanswered questions and uncertainty” unless police were given certain immunity.

The Scottish Police Federation’s lawyers are seeking an undertaking that no evidence given to the inquiry will be used as evidence in a criminal case.

The inquiry’s senior lawyer, Angela Grahame QC, said: “Witnesses are more likely to be frank and honest with their inquisitor if there will be no adverse consequences to them arising from their evidence, such as the use of their evidence in a criminal prosecution or disciplinary proceedings against them.”

Opposing the proposals, Claire Mitchell QC said: “The family of Sheku Bayoh have a legitimate expectation that police officers will give every assistance after a serious incident.

“And that expectation extends to come into a public inquiry and answering all and any legitimate unreal event questions put to it by the inquiry.”

Lord Bracadale said he would consider the arguments and announce his decision “as soon as I can”.