It said the decision had been made after a “thorough review” but added a prosecution could be brought in the future if new facts come to light.

The Scottish Police Federation, which represents 18,500 police officers, said it would welcome an inquiry into the incident.

A spokesperson for COPFS said: “The Crown appreciates that the time taken to conclude this investigation has been difficult for all those involved.

“Following careful consideration and thorough review of all the available evidence, including submissions made on behalf of the family of the deceased, independent Crown counsel has concluded there should not be a prosecution in this case.

“The family have been provided with detailed information about this decision and the review process.

“Although the evidence currently available would not justify criminal proceedings, the Crown reserves the right to prosecute should evidence in support of that become available.

“The Crown is committed to ensuring that all the facts and circumstances surrounding the death of Mr Bayoh are fully aired in an appropriate legal forum.”

David Kennedy, deputy general secretary for the Scottish Police Federation, commented: “We continue to support the officers involved in this incident and hope any public or fatal accident inquiry follows as soon as possible for all the parties involved.”

Deputy chief constable Fiona Taylor said: “Our thoughts remain with Sheku Bayoh’s family and friends following his death and we continue to offer support to anyone affected by this tragic incident.

“We have been committed to co-operating with the Police Investigations and Review Commissioner (PIRC) and the Crown Office throughout this process and will continue to engage appropriately with any further proceedings.

“All deaths in custody trigger a fatal accident inquiry, held before a sheriff into a sudden or unexplained death. It does not seek to apportion blame. Public inquiries, which are rarer, are usually presided over by a judge and only held if there is significant public concern over an event. The decision over whether or not there should be a public inquiry rests with the Scottish government.”