In April the new 'spare bedroom tax' comes into force, meaning many low-income families and disabled people will be forced to move or face yet more cuts. The implications are frighteningSee a summary of the live Twitter chat with @Claire_phipps on #gdnchat and find out how to take part in the next chat about welfare reforms here

The Holden family live on the end of a terraced street in the middle of Hartlepool. There are six of them: Stuart, 36, his wife Lorna, 33, and four kids: Faith, 8, Noah, 6, Elijah, 2, and Sam, 4.

You'd think of them as a thoroughly ordinary family, finding their way through the kind of trying circumstances that now seem to define the national condition, were it not for one detail: Sam, is autistic, and just starting to talk. "He was very non-verbal: shut off," Lorna tells me. "Now, he's starting to communicate what he wants. But it's still only one or two words at a time."

Stuart works a 9.30am-2.30pm shift at the HQ of Student Finance England in nearby Darlington, so as to be around for the more trying parts of the day. Though she aims to return to paid work once she's somehow got round the steep cost of childcare, Lorna – a native of Cambridge, who came to Hartlepool due to a past relationship – has recently been suffering from stress-related illness, as well as gall bladder problems. The family are entitled to £114 a week in housing benefit, which covers their five-bedroom home, rented from the Endeavour Housing Association. All the bedrooms are used: the smallest, they tell me, is a "sensory room" for Sam, where he can let off steam and be free of the overstimulation that can make autistic people extremely distraught.

Their house is sparsely-furnished and slowly being redecorated, with some laminate flooring paid for by Stuart's mum. It's eye-wateringly expensive to heat, they tell me – but since they moved here a few months ago from their previous three-bedroom home, Sam is apparently transformed: "He's like a different kid. He wants to be with you more, he brings you things to read or to look at," says Lorna. But there's a big problem looming. In April, the housing benefit paid to families like the Holdens will be changed by a new set of rules, outlined in last year's Welfare Reform Act.

What's about to arrive is widely known as the "spare bedroom tax", and is a central part of the government's radical changes to social security (which also include a planned real-terms cut in most working-age benefits). It's targeted at what officialspeak terms "under-occupation": if you live in social housing and are deemed to be one bedroom over, your housing benefit will be docked by 14%; if it's two or more, 25%. As a result, hundreds of thousands of people who live on very tight incomes are faced with a choice: either stay in their homes and somehow find the money, or move somewhere else.

For the Holdens, all this is very bad news indeed. With Sam and Elijah sleeping in the same room, and the other two kids each given a bedroom of their own, our initial conversation revolves around the assumption that they'll get a special dispensation for the sensory room – but the new rules still mean that, until daughter Faith turns 10, they'll be "under-occupying" by one bedroom, and therefore in line for a £16 a week hit. To some, that will not sound like much, but like so many families, they count every penny – and the extra money, Lorna tells me, will have to come out of their food budget, which currently runs to around £80 a week, and is largely spent on the budget lines Lorna calls "value food".

"Sam has very specific needs: there are lots of things that he needs – like nappies," says Lorna. "And we can't cut it from fuel, or electricity, or petrol. So when you lay that budget out over a month, with your council tax and water, and all your bills, there's nowhere else it can come from: the only place we can cut from is our food budget. And we're already having the cheapest food you can buy.

"I try and budget each day, like a daily allowance," she says. "So it'll just mean that when the yoghurt's gone, it's gone, and when the fruit's gone, it's gone. We'll just have to go without things: that's just the way it's going to have to be."

Towards the end of our conversation, there comes a grim twist. Contrary to their belief that they will only be penalised for one bedroom, the PR from the housing association raises the possibility that Sam's dedicated sensory room might be deemed to be "spare", meaning that the Holdens will be two bedrooms over their threshold, and faced with a hit of £28 a week.

Suddenly, Lorna looks panicked. How, I wonder, will they be able afford a cut of that size? "I don't think we could," she says.

The government's official blurb says the spare bedroom tax is intended to "contain growing housing benefit expenditure, encourage greater mobility within the social rented sector, make better use of available social housing stock, and improve work incentives for working-age claimants". It makes rules on housing let by councils and housing associations even tighter than similar regulations covering privately rented accommodation – and in that sense, drastically weakens the "social" aspect of so-called social housing.

The new regime is exacting, to say the least. If you're a separated or divorced couple who share the care of your children, only one of you will be allowed extra rooms; if the other keeps a bedroom for the kids, it'll still be deemed "spare". If a family contains two children of the same sex under 16, they must share, and the same will apply to mixed-sex children under 10. As the Holdens have discovered, whether a disabled child is entitled to a room of their own is a matter of some uncertainty, apparently being left to local authorities.

There will be no exceptions for foster carers, who might need extra space for children they look after. Even if a family or couple has had a house or flat kitted out with must-have facilities for someone who's disabled, if they're deemed to be under-occupying, they'll still be penalised (to help such people pay the rent, the government has set aside an extra £30m a year for discretionary payments, though help will be given on a temporary basis, with no kind of hard entitlement – and besides, next year's extra funding set aside to deal with the fall-out from housing benefit cuts amounts to just 6% of what the government intends to save).

The spare bedroom tax will affect around 660,000 households. It's estimated that around two thirds of those households will have at least one person with a disability. In general, one thing seems beyond doubt: the huge national housing shortage means that the government's imagined spurt of mass downsizing simply cannot happen – the Holdens, for example, have asked their housing association to look into the availability of four-bedroom places, only to be told that there's a very long waiting list.

The changes will hit the north far more than the south, chiefly because social housing in the UK's old industrial centres is often synonymous with bigger properties, and there has never been big demand for one- and two-bedroom flats. In that sense, the spare bedroom tax chimes with rising resentment about how disproportionately the government's mixture of cuts and "reform" are hitting different parts of the country. The north/south factor also explains why this most remarkable of stories has barely broken through into the national media – which, according to those who are having to spread the word, means plenty of the people who'll be directly affected seem to be barely aware of what's about to happen.

Five minutes from the Holdens' house, I meet 24-year-old Jason Gaffney. He's unemployed, and on the government's work programme. His flat has two bedrooms, one of which he uses as a compact studio: he's a talented artist and sculptor with A-levels in art and fine art, who says he wants to become self-employed and sell his work – fantasy-based stuff full of psychedelic elements redolent of Grateful Dead albums – online.

Jason Gaffney in his two-bedroom flat in Hartlepool. He uses the spare room as his studio

His jobseeker's allowance brings in around £100 a fortnight, and housing benefit covers his £300-a-month rent. But he's deemed to be one bedroom over, and must therefore find an extra £56 a month. "They're telling me to budget, saying I'm going to have to tighten my belt," he says. "What belt? We've already tightened our belts.

"If I'm going to get even less now, where's that going to leave me? " he says. "What will I have to cut back on? Food. And heating. I hate paying for heat. I've run up debts on heat. And water."

The government's essential idea, I remind him, is that he should move to a one-bedroom flat. "What one bedroom flat?" he shoots back. "There are no one-bedroom flats, that's the thing. They haven't been built. I've asked the housing association that. They don't exist." He could conceivably find a one-bedroom place on the local private rental market, but a quick trawl online suggests that it would cost a minimum of £350 a month, which would actually put his housing benefit up.

Such is the mess of contradiction and impossibility the spare bedroom tax has kicked up. In Manchester, a call to a local councillor leads me to the Mosscare Housing Association, and Tola Adesemowo, their housing services director: she tells me she's taking on extra staff to deal with the fallout from the bedroom tax, and that most of her affected tenants either can't or don't want to move – so, to enable them to take the financial hit, the association has been referring some to food banks.

In Leeds, a spokesperson for the city's Tenants Federation tells me about one particularly remarkable aspect of the spare bedroom tax's consequences: the fact that the city council long ago decided that flats in the upper reaches of tower blocks were ill-suited to families, and let them to single people and couples – who moved in good faith, but are now being hit by the spare bedroom tax en masse. The whole thing, he tells me, is "time bomb waiting to go off".

Talking to people who are anxiously awaiting the spare bedroom tax's effects, questions extend into the distance. What, some wonder, is to stop people claiming a bedroom is a study or home office? "We are not defining a bedroom," says a statement sent my way by the Department of Work and Pensions. "A tenancy agreement normally states the numbers of bedrooms within a property, and the rent will reflect this."

How will people's use of bedrooms be monitored? "It is a responsibility of the claimant to inform us of the size of a property and those living in it," the same text goes on. And what of the chronic shortage of smaller properties in such places as Hartlepool? In response to this question, I get a remarkable reply: despite the fact that the same statement bemoans people living "in homes that are too large for their needs", it also acknowledges that "most people will not move" and claims that "there are other options available such as taking up employment, increasing hours worked or taking in a lodger".

As the other cuts to benefits are also on the way, there's high anxiety among councils and housing associations about massive increases in rent arrears, which will have one simple upshot: fewer houses will be built. And underneath just about everything you hear about the spare bedroom tax lies one rather chilling augury of the UK's future: the fact that, for a swathe of Britons, the certainty of a stable and enduring home is now apparently out of bounds, and family life will in future take place against a backdrop of uncertainty, anxiety and the heavy hand of government.

Back in Hartlepool, Stuart and Lorna Holden tell me there's a lot of local talk about how to beat the spare bedroom tax using the simplest of expedients: human reproduction. "My personal opinion is that if you start adding bedroom taxes on and saying, 'You're under-occupying', people are just going to occupy that space by having more kids," says Lorna.

"I've heard people saying that," says Stuart. "'We'll just have more kids then. We'll fill the bedroom.'"

"And then they get more benefit from the government because they've got more kids," says Lorna. "So what they're really doing is punishing people who are trying to work, and bring up a family, and who need that extra bit of support to make ends meet. I just don't see how it's going to work."

• This article was amended on 25 January, to correct the suggestion that elderly people would be affected - in fact the new tax will not apply to pensioners - and to correct a statistic on the number of people affected.