Former cabinet minister Jonathan Aitken is drawing on his personal experience of befriending and helping a former prison inmate to quit crime and find a stable job, as he calls on ministers to establish a new national network of 15,000 mentors to slash reoffending rates.

In a report on mentoring for the Centre for Social Justice thinktank, Aitken tells for the first time how he helped Leroy Skeete, a fellow inmate in Belmarsh prison in 1999, where Skeete was serving an 11-year sentence for aggravated bodily harm, to end his cycle of reoffending and find full-time work a decade later.

Aitken, who says the government could cut the £11bn-a-year cost of reoffending by at least £1bn if it overcame resistance from the probation and prison services and organised mentoring properly, tells how Skeete had all the hallmarks of a serial offender when he first met him, but had the drive and will to turn his life round with the help of friends.

"We were fellow prisoners in House Block Three," Aitken writes. "We got on well in that environment but I would not have been optimistic about his prospects for ceasing to reoffend. He came from a broken home and was poorly educated … and his general attitude was that of a serial offender."

To Aitken's surprise Skeete contacted Aitken – who was jailed for perjury and perverting the course of justice in 1999 and was released in 2000 – after he ended his sentence in 2007 and they agreed to start a mentoring relationship.

"The factors which, in my view, made the relationship succeed was that we had met in prison; that we both understood the difficulties of starting life again as an ex-prisoner ...," Aitken says in the report. "We met about once a week. A lot of our early time together was spent listening to Leroy's problems. I taught him how to write a CV and rehearsed job interviews."

Together they found Skeete work as a driver and a wine waiter before Aitken introduced him to a charity called Blue Sky, which specialises in finding employment for ex-offenders. After 15 months he was put in touch with a company employing night maintenance workers on London Underground and soon after was given permanent employment. Two years later he was married and has not reoffended. In the CSJ report Aitken argues that a combination of professional and voluntary mentors, who would start visiting prisoners before their release and continue after, could cut re-offending rates dramatically. They could be paid for out of a new £450m annual budget that the government has allocated to 21 companies dealing specifically with the rehabilitation of offenders.

Currently 58% of prisoners sentenced to less than 12 months in prison re-offend within a year of release. The report says there is a high number of potential mentors willing to volunteer but argues that their recruitment is being held back by the low number of referrals coming from the prison and probation services.

While mentoring was once an integral part of the probation service it has fallen out of fashion as volunteers have been "pushed aside by jobsowrths, who bureaucratic expansionism made them determined to suppress the work done with offenders by anyone not on the official payroll," Aitken says.

Most mentors now work for charities and are paid for by non-government bodies. Currently there are around 3,000 mentors in England and Wales of whom around 90% are part-time volunteers.