Bruce spits out his stories in fragments not sentences. Dates are missing, details go awol. But you listen anyway because he’s got some tales, and he knows it. Like the one about the time he died. Steaming drunk, he’d been arrested. Back then, Bruce would drink or take anything he could get his hands on. Methylated spirit and aftershave. Tranquillisers and magic mushrooms. He’d sniff petrol and glue, which made him feel “like a rubber band”.

This time, he’d drunk so much he fell unconscious in a Staffordshire police station and “swallowed my tongue”. He stopped breathing, the vital signs went, and for a while they thought he was dead: “Paramedics brought me round in A&E.” Lazarus showed neither gratitude nor wisdom. “I was violent, so I got rearrested.” Years later, the memory makes him cackle.

After being slung out of the family home as a teenager, Bruce spent nearly 30 years homeless and saw a lot of police stations and hospitals. He stayed in so many prisons he can rattle off an itinerary: the juvenile lock-up at Werrington, near Stoke, when he was growing up. Strangeways, Lincoln, Stoke Heath, Dovegate, Risley, Walton … When an older sister died of breast cancer, he attended her funeral in handcuffs.

Detox units took him in – then lobbed him back into his old world, where he could start drinking all over again

Most nights, he slept rough: up on roofs in freezing winds, down by the River Trent under damp railway arches, in the giant abandoned kilns that still dot the Potteries. Monasteries and convents would give food and shelter. Most of all, Bruce kept on the move: “I could walk the mileage, mate: 40 miles a day, seven days a week. I could walk the planet.”

He, his partner Louise (not their real names) and their Jack Russell terrier Skip would walk from coast to coast, from Newcastle right down to Great Yarmouth. “I love London,” he says. “Haven’t been back for years.” And for a moment he sounds like a tourist rhapsodising over some golden holiday, except his landmarks aren’t in any Lonely Planet. “Cardboard City: stayed there.”

For decades, this was his life. Authority figures were either useless or positively harmful. His mum walked out when he was four; later, he and his brothers and sisters were sent to an institution in north Wales. “Like a mental asylum. Like One Flew Over the Cuckoo’s Nest. Abuse?” Now he’s shouting. “You wouldn’t know what it was. And you wonder why I cracked.”

Prisons released him straight out on to the streets. Detox units took him in, cleaned him up – then lobbed him back into his old world, where he could start drinking all over again. After a concrete block fell on his leg and shattered it, a hospital fixed up his shin – then discharged him with a Zimmer frame but nowhere to sleep. A therapist expected him to shuffle along the streets with all his gear plus some NHS-issue aluminium. “Fucking useless.” It was swiftly donated to the nearest canal.

Tonight in one of the world’s richest countries, more than 300,000 people won’t have a home to call their own. They will sleep instead in temporary accommodation, in homeless hostels, in rooms provided by social services – and in the worst case out on the streets. Since 2010, the official number of rough sleepers like Bruce has soared 134% to 4,751 – and that is almost certainly an underestimate. The charity Crisis puts the number at 8,000 in England alone, with a further 8,000 seeking refuge in tents, cars and on buses and trains.

Their stories rarely end happily. Most of the rough sleepers Bruce knew are now dead. On the streets, a man can expect to die at about 47; for a woman sleeping rough, death comes more quickly, at 43, compared with 83 for the average British woman.

At 51, Bruce is beating the odds. Having spent most of his life unsure where he’ll sleep, he now has a home of his own. Come Christmas, he’ll have been in his one-bed flat for five years. The coffee table, the sofa and most of the rest were bought with his own cash. He gets his groceries from Asda and knocks up a decent curry. The day we meet, he’s looking forward to Emmerdale: “It’s getting good. Lachlan’s on a mission.”

In a neat black shirt and with sandy hair turning the colour of salt, the only immediate giveaways of his past life are the self-harm scars that ladder both wrists and the way he comes in and out of lucidity, like sunshine on a cloudy autumn day. But after decades of being ignored or abused, of drinking himself nearly to death on any cut-price poison, his life is now almost as uneventful as yours or mine.

How did this happen? The simple answer is politics. Or, to be more precise, a policy called Housing First. It has been adopted by Finland, Denmark, Spain and France, as well as parts of the US and Canada. In every country, the transformation has been astonishing. In the UK, Labour likes the idea, and the Tories are piloting it. But while Westminster makes warm noises, some councils and local groups are getting on and doing it. In Stoke three years ago, the Voices partnership used National Lottery funding to commission a Housing First programme. Among the first on it was Bruce.

Housing First argues that the main thing a homeless person needs is a home. Give that and dedicated support to help someone adjust to a new way of living, and the rest will slowly fall into place. The drug taking will go down, the illnesses will get less frequent and less serious. And time after time it works. Yet however simple that sounds, it’s the opposite of how homeless people are usually treated.

In London and Manchester, property developers keep people from sleeping in their doorways by putting up metal spikes. Those bedding down in Bournemouth coach station have been blasted with bagpipe music, by order of the council. Last winter, a Torbay businessman stuck up pictures of people he said were “professional beggars”. And Stoke council was last year planning to fine rough sleepers £1,000 each – until critics pointed out that if they had a grand spare, they probably wouldn’t be on the streets. Underpinning all this casual cruelty is a prejudice that says Britain is a property-owning democracy, and those without a property don’t deserve full democratic rights. It’s an attitude that runs wide and deep, to some of our most basic services.

This spring, researchers in Stoke found that barely one in four local GPs were willing to register homeless patients without restriction. Practices would demand someone of no fixed abode provide a utility bill with an address – or simply refused to treat them. This is despite the Care Quality Commission saying it “expects practices to register people who are homeless” and even advising them to put down the surgery’s address on registration forms.

To stand a chance of securing stable accommodation, homeless people across the UK usually need to prove they’re “housing ready”. Lay off the booze, and you too might win a “transitional unit”. Opposed to that system is Housing First, where you don’t earn a roof over your head but are treated as if you’re entitled to one.

As the most enthusiastic adopter of Housing First, Finland is the only European Union country where homelessness is not rising but falling – by an average of 35% between 2008 and 2015. The problem of rough sleeping has to all intents and purposes been solved.

Along with his new flat, Bruce got a support worker, Tim Ditchfield. After hanging out for almost five years, they know each other like friends. At the beginning Ditchfield planned what Bruce needed to live his new life the way he wanted. And he argued with doctors and therapists and officials to get him proper support. “Together, we try and get round the gatekeepers,” Ditchfield says.

Ditchfield introduced Bruce to charity shops, which is where most of his furniture comes from. And Bruce has responded to the trust placed in him. He pays all his rent in cash, three months up front. He has barely used the discretionary fund available to local Housing First tenants: with only the modest benefits owed to him, he has constructed a tightly budgeted lifestyle.

The stability that comes from having a roof over his head has spread to all parts of his life. While he still drinks, Ditchfield says “he is not obliterating himself any more”. Most striking, Bruce is now saving up for a bungalow to get away from his noisy neighbours. “I want tranquillity now, mate.”

In the year before Bruce moved into his flat, he was in A&E 20 times; spent one night as a hospital inpatient; was arrested twice; appeared before a magistrate once; was convicted once; and was in a cell for two nights. Going by official calculations for the cost of each of these, Bruce put £5,139 worth of demand on our public services.

Over the following three years, he did none of these things – apart from one spell when he was in and out of A&E a few times. But no serious illness, no law breaking, no prison. Plus: no use of police time, no grief from the council, no damage to property. And he is entirely typical. The support of Ditchfield and his colleagues costs, but a York University study of nine Housing First schemes in 2015 estimated that the policy offered “overall savings in public expenditure that could be in excess of £15,000 per person per annum”.

The policy doesn’t work for everyone. Running the Housing First programme in Stoke, Jane Turner also knows its pitfalls. Some rough sleepers can’t cope with bill-paying domesticity. Others find that their old mates from the street move in and cause havoc. Having worked at a homeless hostel for five years, Turner knows their advantages. Security, three hot meals a day, regular check-ups. She also sees when they fail: “You get people coming into hostels, going through them and out – and then coming back again.” At the hostel where she worked in the late 1990s, she sees some of the same rough sleepers she saw 20 years ago. Without Bruce’s luck, they haven’t broken out of the life-shortening vicious cycle.

The charity Crisis believes Housing First could help more than 18,000 people in Britain – not just rough sleepers, but other people with complex housing needs. When the Finns made this a national strategy, they also built thousands of low-rent flats. In Stoke, they rely on housing associations and private landlords. When Ditchfield’s colleague Mike Goodwin rings round letting agents, they say: “No DSS”. Or they demand six months’ rent up front. The result is that Turner has 10 people waiting to be housed.

On the floor of Bruce’s living room are a few laminated photos of his dad’s grave. After hearing him talking about his dad so often, Ditchfield drove Bruce to see it. They bought flowers from the local shop, crouched silently at the graveside, then, remembers Ditchfield, “sat like a pair of old blokes on a bench, reminiscing about old times”. The pictures were given to Bruce as a reminder of that day.

You would never get that in the normal run of public services – and that is what makes Housing First so alluring. It is a reminder that the welfare state doesn’t have to be mean and pinched. That the only reason families wait years for a home, or sick people get only 10 minutes with a GP, is because successive governments have refused to put the money in.

Like universal basic income, Housing First is as much a challenge as a policy. What if we were to say that poor people aren’t poor because of a character flaw but simply because they don’t have money? What if homeless people deserve a home, as the UN says is a universal right? What if those who need help from the state got it, rather than incessant bullying?

“Housing First makes politicians nervous. It smacks of queue jumping,” says Andy Meakin, director of Voices. But it’s more radical than that: it raises the question of why there should be queues for an essential like housing.

Underneath those graveside photos is another laminate: a letter from Bruce to his partner. It dates from when they were in the same mental health hospital but could barely see each other. In Bruce’s handwriting, neat and round, it reads: “I still love you in my heart, as a friend, partner, I know you feel the same way … lonely and lost, your [sic] the only person I care for, you deserve a better life … your [sic] my Bonnie Louise.” Along the bottom runs the acronym SWALK.

Louise and Bruce, Bonnie and Clyde. Together for 30 hard years. Let’s hope they get the chance to turn into a pair of boring old sods.

• Aditya Chakrabortty is a Guardian columnist and senior economics commentator