Lord Bracadale, who has led the public inquiry since 2020, said the participation of Mr Bayoh’s relatives was essential and defended the five meetings as “private but not secret”, insisting they were not unfair to the inquiry process.

Mr Bayoh, a 31-year-old father of two, died in May 2015 after being restrained by six police officers in Kirkcaldy. The inquiry is examining the circumstances of his death, how it was handled by police and prosecutors, and whether race was a factor.

The SPF, which represents rank-and-file officers, had claimed the meetings “torpedoed the independence of the chair” and raised concerns that other core participants had not been informed. It is understood the organisation is considering a judicial review of Lord Bracadale’s decision.

In a statement issued after a June hearing where all parties gave their views, a spokeswoman for the inquiry said: “After careful consideration of written and oral submissions from core participants, Lord Bracadale has decided not to recuse himself or terminate the appointments of the assessors.

“Having regard to the relevant legal test he has determined there is no apparent bias.

“Taking into account various considerations in respect of the handling of the Inquiry, he has determined having meetings with the families was not unfair.”

An SPF spokesperson said: “Any fair minded observer would be concerned when it is revealed that there have been five meetings with a core participant family, without the knowledge of the other core participants.

“The inquiry’s legal team asserted that no evidence was discussed at these meetings, it subsequently transpired that was not the case. Police officers will continue to call for a fair and transparent hearing, based on the evidence alone.”

Lawyers for the SPF told the June hearing that the meetings were “in almost their entirety, completely inappropriate”.

Deputy First Minister Kate Forbes said: “I note the detailed and extensive consideration that has informed Lord Bracadale’s decision and hope all parties involved can progress the important work of the inquiry as soon as possible.

“The Scottish government remains committed to establishing the facts surrounding the circumstances leading to Mr Bayoh’s death. However, as it is vital all public inquiries operate independently of government, it would be inappropriate of me to comment any further.”