In a little council house in Birkenhead, Steve is panicking over how he’ll find an extra £304 rent money a month. He has just days to magic up an answer. If he can’t, he can guess what will happen. “Eviction. Come the end of November, I won’t have a roof.” As a single parent, Steve won’t be the only one slung out. His four boys, aged from three to eight, would also lose their home and probably be taken from their dad. “I’d be fed to the dogs.” Everything I’ve tried so hard for …” – a snap of his fingers – “Nothing.”

It’s not a landlord doing this to Steve; it’s our government. It’s not his rent that’s going up; it’s his housing benefit that’s getting cut. And he’s not the only one; on official figures, almost 500 households in the borough of Wirral face a shortfall of up to £500 a month.

From next Monday 88,000 families across Britain will have their housing benefit slashed. They will no longer have the cash to pay their rent. Among all those whose lives will be turned upside down will be a quarter of a million children. That’s enough kids to fill 350 primary schools, all facing homelessness.

Those figures come directly from the Department for Work and Pensions. Plenty dispute them, which is unsurprising since DWP officials keep changing their minds. Some experts believe the number of children at risk could total 500,000.

This is the biggest benefit cut that you’ve never heard of. The newspapers will waste gallons of ink on Candice Bake-Off’s lipstick and Cheryl’s apparent baby bump. But about a government policy that could disrupt hundreds of thousands of lives, there is near silence.

So allow me to explain. From next week Theresa May’s government will extend the cap on household benefits. Poor families in London will not be allowed more than £442 a week. Those outside the capital will be cut to £385 a week. In some areas the cuts will be brought in straightaway; in others with a slight delay. But in the end, families above the limit will be hit twice over. First, they will be pushed further into poverty. And, like Steve, their housing benefit will be docked, so they will be left scrabbling just to make the rent and keep a roof above their heads.

How those families will manage is anyone’s guess. When Steve opened the letter at the end of July he had a “panic attack”. All that went round his mind was one question: “How the hell am I going to pay this?” Then came what he calls “a depressive state” that lasted nearly two months. Now he bottles it up, for the sake of his boys. “When they’re not around, that’s when I cry. When they’re out at school, when they’re asleep: that’s when I break down.”

It’s the fear of losing the boys he fought so hard for custody of that haunts him most. So worried is he about a social worker taking them away that he requests a false name.

Like many of the families that will be hit, Steve’s options are very limited. He can borrow from his mum, although she’s hard up. He can try to land 16 hours’ work a week – and has already been giving out his CV – but not too many employers will be able to fit around his school runs and meal preps. Or he can ask Wirral council to top up his rent, by filling out a complicated form that asks for proof of his weekly spend on everything from cigarettes to toiletries. And that would only cover him for a few months.

He has one jumper and one coat to last him the entire winter. He sometimes gets by on a single bowl of cornflakes a day

Even before next week’s cuts, Steve is already bumping along the bottom. He has one jumper and one coat to last him the entire winter. He sometimes gets by on a single bowl of cornflakes a day. Anything spare goes towards the boys. But they don’t get fresh fruit or veg, subsisting on frozen meals from Iceland.

The three-year-old comes into the kitchen for a drink, and as Steve opens the fridge, I can see it contains nothing apart from a half-full bottle of milk. The house is empty to the point of desolation: no shades for any of the lightbulbs, none of the usual family photos or decorations.

George Osborne’s benefits cap was always a rotten policy that played well in focus groups. But when introduced in 2013, it hit a relatively small number of poor families in high-rent London. And, some on the right would whisper in the ears of biddable journalists, the poor really had no place in the world’s biggest property bubble. The cuts that start next week will be a step change. They will hit low-rent areas such as Wirral and Darlington. They will render family homes rented out by housing associations “financially toxic”, according to the housing expert Joe Halewood: tenants will no longer be able to afford them, and housing associations can’t afford to leave them empty. And they will rip through the budgets of already cash-starved local councils, who will now have to find emergency accommodation and cash funds for displaced families.

To see how deep it will cut, have a look at these figures. I grew up on the outskirts of London, in a place called Edmonton. It has pockets of deprivation as bad as anything in Wirral and, on DWP estimates, around 1,200 households here will be hit by the new benefits cap. By my reckoning, this government now expects children growing up in my former home to be raised on £1.02 a day.

The basic expenses for a family with four children in Edmonton come to £399.14 per week.

My sums go as follows:

£315.12 for rent (the allowable local rent for a three-bed home).

£33.36 for council tax (Enfield council, band E property).

£32 for gas and electric (the average weekly bill, according to government figures, with an extra 20% added for a large family).

£8.54 for water (Thames Water’s average bill for 2015, with 20% added for a large family).

£10.12 phone and broadband (BT Anytime standard package).

Taking all that from the £442.31 allowed to any London family leaves £43.17 each week left over for the family. That is £1.02 per person per day.

Of course, these figures are arguable. The family could cut down on energy use by choosing to be cold this winter. Or they could go without showers and washing up. That said, I’ve left off mobile phone calls and TV. I’ve not factored in school trips or family breaks or Christmas.

These cuts will do something Thatcher never managed: they break once and for all the link between the needs of benefits claimants and their entitlements. Children will be punished for the “sins” of their parents: the sins of being poor and of having too large a family in the eyes of Osborne and Iain Duncan Smith. David Cameron’s Tories once legislated to “eliminate child poverty”: Theresa May’s Tories are re-creating it for a new generation.