I first entered the penal system in England in 1957. Then, over the next four decades, I was in and out of prison and endured it with as much good grace as possible. For the last 16 years, I have written about the system that incarcerated me, and I watch films, documentaries, indeed, any performance that promises to depict jail life as it is and offers lessons in how to improve it for prisoners and the public.

More often than not, I am disappointed. But occasionally, I find a nugget like Second Chance, a film by Rex Bloomstein, who has form for reporting accurately and powerfully on the criminal justice system in this country.

It features jails and prisoners but, at a time when the prison system is in meltdown and reformers in despair, it offers a glimpse of hope and inspiration and, above all, shows what can and should be done if we are to make headway in the battle against reoffending. This is a fight we are clearly losing. No amount of tough talk by Boris Johnson or his home secretary, Priti Patel, designed to win over Brexit party supporters in the run-up to an election will reduce reoffending, which costs taxpayers about £15bn a year. More than half of all adults leaving prison are reconvicted within a year of discharge. Two-thirds of those had failed to find work on release.

Can we claim surprise at these figures? Without a job, or home in many cases, and a discharge grant of £46, – unchanged since 1995 – where else can most ex-cons drift back to, but crime? Most of those who find work do not reoffend, yet many employers are reluctant to take a chance with former prisoners.

Second Chance follows the fortunes of six people who were convicted and jailed for criminal offences: four former prisoners in work and two hoping to join them. They are the products of a bold scheme that has achieved staggering success rates since it began. James Timpson, who runs the family-owned shoe-repair and key-cutting chain, says he has employed 1,500 ex-prisoners in his shops since launching the venture and just four have gone back to prison. I repeat that: four out of 1,500. These are figures to die for even for those forward-thinking Scandinavian countries. These are not northern European success rates, they are utopian super-statistics.

Timpson realised there was a wealth of talent behind bars, so in 2008, he opened a training academy at HMP Liverpool. The Timpson group, which also owns the dry cleaners Johnsons, and Snappy Snaps and Max Spielmann photo shops, now has workshops in seven prisons, along with a Max Spielmann academy in New Hall prison, west Yorkshire. And there are plans in place to roll out the scheme across all the outlets in the group, including the dry-cleaning chain.

You could be forgiven for thinking Second Chance is merely great PR for the company. But Timpson says the staff he recruits from prison are among the most loyal and honest of all his employees. It takes some bottle to tell your half a million customers, whose shoes you repair, keys you cut and photos you process each week, that you recruit from prisons. This absorbing film sends the message out – quietly but clearly. The prime minister would do well to listen.

• Eric Allison is the Guardian’s prison correspondent