Staff cuts in jails are making it increasingly difficult for prison officers to tackle the problem of Islamic radicalisation among inmates, the former head of the National Counter Terrorism Security Office warned.

Chris Phillips said there were not enough prison officers to properly monitor extremists in jail, meaning they were able to intimidate and recruit other inmates.

"What we have actually is a prison population that's growing," Philips told the BBC. "We have less officers generally in prisons than ever before and we also have less police officers to deal with them, so what we have is a growing haystack of extremists where we still have to find the single needle that's going to go off and do something really nasty.

"But of course we've got less people to go and look for them as well so it's a really difficult thing for the police service and prison service to deal with."

In March, a report by the Justice Select Committee criticised the government for cutting staffing levels in prisons, and said 12,530 prison officers, or 30% of its total, had been cut between 2010 and 2014.

The UK now has a Muslim prison population of more than 12,000, with 100 jailed for terror offences.

But Justice Secretary Chris Grayling said there was "no evidence" to support Phillips' claims. "Prison overcrowding is at virtually its lowest level for a decade, and we have increased spending on measures to prevent radicalisation," he said. "We will never be complacent about the issue."

In 2014, sources from the prison officers union told the Daily Mirror that Islamic radicals in prisons including HMP Whitemoor in Cambridgeshire, where several high-profile terrorists are locked up, were violently intimidating inmates to force them to convert. "Whitemoor is now effectively run by Muslims, many of whom are jihadis," said one source.

Michael Spurr, the chief executive of the National Offender Management Service of England and Wales, warned there was a risk of a prisoner radicalised behind bars carrying out a terror offence.

He said: "There is a significant risk, given the fact that we manage some very dangerous people. Our job is to minimise that risk becoming a reality – that somebody in prison becomes radicalised and commits a terrorist offence."

Dame Anne Owers, in a 2010 report, wrote that while Muslim inmates may be more susceptible to extremism, unfair suspicion of Muslim prisoners is unfair and can drive them into the arms of extremists.