The former Tory minister George Young described the homeless as “what you step over when you come out of the opera”.

No, Sir George: today’s homeless deliver your takeaways and pull pints at the local. Then they kip on park benches.

Martin, who works for Islington council taking disabled children to school, told me how he’d spent a month sleeping either in Hampstead Heath or by the canal near London Zoo. “I was exhausted all the time,” he said. Some mornings, he’d knock for the children still clutching the bag that held all his belongings.

This month, the charity Shelter calculated that over 170,000 Londoners are homeless. Its researchers pieced together the data for how many were both in a job and in temporary accommodation: it amounts to nearly half (47%) of all homeless households in the capital.

Figures like these, and shelters like Scott’s, neatly puncture many of the official boasts about work in post-crash Britain. The ministerial bragging about record employment? That economic miracle would include a third of the people dossing down at Scott’s place. The smugness with which David Cameron talked about the high-tech sharing economy? The Uber driver in that bunk over there might put him right on a few things. All the blether about how strong unions will destroy the economy? The casualised workforce in these improvised dormitories make a good argument for labour protection.

Most of all, it proves that two of the hardiest orthodoxies in British politics are now a lie. First, the notion that work pays. That is why Norman Tebbit told men to get on their bikes, why Gordon Brown fiddled about with tax credits, why George Osborne could get away with attacking “skivers”. But minimum wages, zero-hours contracts and a couple of shifts through a temping agency don’t pay. They certainly don’t pay enough to get you decent accommodation in one of the most expensive housing markets on the planet.

When that belief dies, so too must its corollary: that the homeless are always unemployed. “Why are beggars despised? For they are despised universally,” asked George Orwell in Down and Out in Paris and London. “It is for the simple reason that they fail to earn a decent living.” None of the people I met were begging, but each lived within the shadow of the idea that by being homeless, they had become despicable.

“I’d always thought homelessness was for alcoholics and addicts,” said Liam. The twentysomething had been an engineer on the London Underground before his subcontractor moved on, leaving him short of work and burning through his savings. Now he does shifts in a pub, earning just above minimum wage. It’s not enough. Before coming to the shelter after each closing time, he’d wander the streets. When Euston station opened around 3.30am, he’d creep upstairs and lie down for a few hours.

Not that he slept much, for all the crying and worrying. The next day would be spent in a youth centre. His mum would ring. “All I wanted to do was to break down and say, ‘Mam, I’ve lost everything now, I don’t have anything left.’ But if she heard that, it’d break her heart.” Like all the homeless people interviewed here, Liam is a pseudonym. For him to talk to me is to relive his humiliations: his face goes red, he stammers and barely ever catches my eye. Yet for all the shame that laces his story, he did nothing wrong. He just turned up for work.

Post-crash Britain punishes workers even as it knights tax-dodging bosses. It applauds zero-hours contracts while it prosecutes begging. It starves those with disabilities into work, knowing the work won’t put food on the table. It trumpets poverty pay as an economic miracle.