Britain's security experts on Monday called for a fundamental review of the threat of radicalisation in the UK's prisons after a media report claimed that the system was not fully cracking down on Islamist extremism behind bars.

Extremists in some of Britain's prisons are allegedly holding makeshift Sharia trials, circulating banned books and openly grooming young Muslim inmates, 'The Times' reports.

A former prisoner who claims he took part in Sharia courts and punishment beatings has given the newspaper a detailed account of how he came to join a group of prisoners at HMP Woodhill in Milton Keynes, south-east England, who pledged allegiance to the Islamic State terrorist group.

The former prisoner, who provided an account of his radicalisation and has been given the pseudonym Jack, said those who recruited him included a follower of the convicted Pakistani-origin radical preacher Anjem Choudary, out on licence or parole under strict conditions since his release from prison last year.

Richard Walton, former head of Scotland Yard’s Counter Terrorism Command, and Ian Acheson, who led a previous review of jail extremism in the UK, said that reforms to tackle the problem of extremism in jails had stalled.

"I'm disappointed that many of the recommendations I made in 2016 to robustly respond to this threat do not seem to have been adopted. This implies a continuing serious failure of leadership and will to confront terrorism that I identified," Acheson told the newspaper.

"I urge the government to return to these recommendations as a starting point to check on the reality of counter-extremism capability. If the Prison Service is not equal to the task of managing this lethal and destructive risk it should be divested of that responsibility," he said.

UK Justice Secretary Robert Buckland said the former inmate's account was "very concerning" but insisted that in the past four years "a great deal of time, effort and investment has gone into bearing down on the malign effects of extremism behind bars".

The issue of extremism in UK prisons came under scrutiny last month when Usman Khan, a 28-year-old out of parole on terrorism charges, went on a knife rampage killing two people and injuring several others on London Bridge.

Khan had been jailed in 2012 for plans to set up a terrorist training camp on his family’s land in Pakistan-occupied Kashmir and it is feared he may have been further radicalised while behind bars.