The people you are about to meet are invisible. Politicians don’t mention them. Much of the media ignore them. I can see why. To say such folk exist is to admit that much more is wrong in Britain than the gatekeepers of our national conversation will allow. It’s to accept that some of our prized insights about the economy are junk, and to understand, however fleetingly, how little stands between the rest of us and complete disaster.

For all that, they are as real as you or me – and they are fast growing in number. They are people who are homeless, even though they are working.

I met some of them last week, at an emergency night shelter in the centre of London. Their jobs are with some of our biggest companies and local councils. At the end of a working day, they come back to this warehouse unit to sleep in a metal bunk bed alongside 42 others. The men share one toilet, women the other. Among the homeless, this counts as a good ticket: Shelter from the Storm provides dinner and breakfast.

Around one in three of the people bedding down here are in work. The night I went, the charity’s co-founder, Sheila Scott, looked down the list of guests and identified their employers. It was a roll call of Britain’s consumer economy: Starbucks, Eat, Pret. A woman who travelled three hours to work at a Co-op grocery. Pubs, McDonald’s, a courier for Deliveroo.

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.

To be poor in Britain is to be treated by public officials and private managers with jovial contempt. Another guest of Scott’s, Nicola, tells me how her landlady went bust and she was evicted in May. Rather than sleep on the streets, she spent nights sitting in a police station. If she nodded off, the officers would blast hip-hop to wake her up. When she sought funds from Haringey council, she says one officer told her, “You don’t even look homeless.” She claims another directed her to take out a payday loan (Haringey denies both allegations).

One job interviewer sussed she was staying in a shelter. He said he’d never seen a homeless person before and demanded: “Give us a twirl.”

Nichola works in a warehouse for Greggs, making cakes and cookies. After nearly two years there, she’s still on a temp contract through an agency. No regular hours, just a text when they want her to come in – to which she has to reply promptly or lose the work.

The shifts typically start at 6am, which means getting up at 3am and taking three buses. A few weeks ago she slogged across London only for the factory machine to pack up. She was paid for the 2.5 hours it was functioning.

When contempt is embedded in the contract, it feeds through to the workplace. At the end of a shift last week, the manager pointed at all the work left over and barked: “You’re not going anywhere.” Greggs says agency staff are generally only employed on a short-term basis. I’ve seen payslips that suggest otherwise. I’ve also seen the company report that boasts of shareholders being paid £43.7m in dividends last year.

Nichola, Liam and Martin will all be spending this Christmas homeless. I ask Nichola how she will spend the 25th. She replies: “Sleep all day. I have not had a proper sleep since May.”