A commentary pointing to expected effects of cuts in state benefits, particularly those relating to housing, said that in Iain Duncan Smith's constituency, 5,110 households in privately rented accommodation would lose heavily. But the constituency of the secretary of state for work and pensions was named as Redbridge, when it should have been Chingford and Woodford Green. The constituency includes a part of the London Borough of Redbridge.

Do they know what they are doing? Are they incompetent bunglers or do they mean to clear low earners out of the country's prosperous districts? As some residents since time immemorial are driven away – with maybe a few picturesque pearly kings and queens among them – this will become a cut that brands this government. Perhaps they think nobody will notice the new ranks of rough sleepers. Or that housing benefit is too fiendishly complicated to understand. Few Conservative voters claim it, and the removals will be an invisible migration, not a mass exodus in special coaches. However, these cuts are so extreme and random as to who will be evicted that the political noise will rise to ear-splitting decibels.

Follow these numbers carefully and see how they multiply upon one another. This month people who lost their job have had their help with mortgage interest payments cut in half. Expect more arrears and repossessions. Next year housing association and council rents will rise from their present heavily subsidised rents to 80% of the market rent for new tenants – about £100 more a week. New social housing will no longer be available to the poorest, but only to those who can pay high rents.

People in private rented accommodation will see their benefits capped from April. From October only rents below the 30th percentile for the area will be eligible. The Department for Work and Pensions says families will pay an average £22 more a week, but evidence suggests in many places it will be far more. But that's only part of it. In a radical change to benefit philosophy, anyone out of work for more than a year will lose another 10% from their housing benefit. This is a departure into the realms of US welfarism, influenced by the architects of American time-limited welfare who have been visiting David Cameron. Conditionality now gives way to punishment, shadow DWP secretary Douglas Alexander points out, regardless of how hard someone tries to find work that isn't there. This arbitrary cut is the first step to an entirely new policy.

But that's not all. The sum paid towards the rent will fall every year, in perpetuity: it will no longer rise as average local rents rise but will be pegged to the consumer price index. If that had happened in the last decade most people would have been priced out: rents rose by 70%, but the CPI only rose 20%.

Now add in something more sinister. Council tax benefit, worth an average £16 a week, is to be cut by 10% and then handed over to each local authority to decide how much benefit to offer: if some councils want to push poor people out, they can pay virtually nothing to their residents. But hey, that's localism. Add up the cumulative effects and there is the biggest welfare cut ever attempted: even Margaret Thatcher was careful never to take benefits away from existing claimants. New claimants don't know what they are missing, but old claimants – especially pensioners – make very nasty headlines indeed.

Ministers know what will happen, since the housing minister has set aside £10m to £12m for "transition costs" – the cost of removing families and their belongings from London boroughs to places like Hastings, or Shoeburyness. London councils told the work and pensions committee that they are already block-booking bed and breakfast and cheap properties in far away places.

London will be hardest hit, but low earners in salubrious parts of the south-west, Bristol, Nottingham, Manchester and anywhere prosperous will also see rent rises that force removals. Those in new jobs will only be able to find homes in districts that are cheap because there is no work. Children will be taken out of their schools, however close to exams they may be. Who will do the cleaning, caring and catering in expensive places once low earners are cleared away?

Karen Buck, DWP shadow minister and MP for the poorer part of Westminster, will see many depart. The borough has 5,300 households living in private rented flats who draw housing benefit, with 6,000 children in Westminster schools. All will face huge rent rises, most will move. How will Iain Duncan Smith explain that his reforms are meant to make work pay when he is forcing people to move to cheap ghettos where there is least work? In his London constituency of Redbridge, 5,110 households in private rentals will lose heavily, 290 of them pensioners: that's the number in just one borough. A family in a Chingford two-bedroom flat will lose £624 a year. Add in another barrier – anyone wanting to work will lose 65p in housing benefit for every pound they earn.

What would Duncan Smith say to the caretaker Buck met? He lives in Brent, one of the third of housing benefit claimants who are in work, and he earns £12,000. But he will lose £80 a week, so he can't afford to stay. He will look for somewhere cheaper, and distant. That means losing his job with its 7am start: Duncan Smith and his "get on your bus" will not get him there in time. Another problem – will this caretaker qualify for jobseeker's allowance, or will the jobcentre say he made himself intentionally unemployed? And has he made himself "intentionally homeless" when he throws his family on the mercy of the council to be rehoused?

The great house price bubble helped cause the crash: US sub-prime loans to the poorest lit the fuse. Labour failed to build enough private or social housing while waiting lists grew. House prices doubled in the golden decade but that unearned windfall for the lucky generation went untaxed. Meanwhile housing benefit claims soared as lack of cheap council housing saw councils put people into expensive private housing instead. The crash meant new claimants among the unemployed and those whose hours and pay were cut. Councils put people into private rentals for lack of cheaper social housing, and of course the number of households is growing as people live longer. The shortage will get much worse with the housing budget halved.

Rent was always the glitch in the benefit system, and Beveridge never found a logical answer. Well, here at last is a final solution he never considered: put all poor people in distant dumping grounds where nobody wants to live because there is no work, then call them workless scroungers, lacking in aspiration for the children they have taken out of class to throw together in schools where nobody's parents work. Might we hear a little less sophistry about fairness from David Cameron and Nick Clegg?