Tens of thousands of low-income families in inner London and other areas of high housing demand will have to move to the suburbs, putting huge pressure on local schools and other public services, council leaders and housing charities warned today in response to the benefit reforms announced by George Osborne.

The benefits of workless families will be capped at £500 per week, the median post-tax income of a working household. The cap, introduced from 2013, will in part be applied through a reduction in housing benefit, hitting about 50,000 families.

These households will lose an average of £93 each week. A tiny number might lose as much as £300. The government would not say how much will be saved, but it is likely to be around £300m-£400m.

The reforms come on top of the cap on local housing allowance (LHA), the equivalent of housing benefit in the private rented sector, announced in the June emergency budget. From October 2011 LHA will be capped at 30% of average local rents, with housing benefit linked to consumer price inflation rather than the higher retail price index, a change due to save as much as £3.9bn.

That cap would put as many as 82,000 households, or 250,000 people, at risk of losing homes in the capital or being forced to move, London councils warned.

Karen Buck, a housing expert and the Labour MP for Westminster North, said it seemed "inevitable" that councils' duties to house the homeless would now be relaxed. She said: "We are going to see some of the largest population movements in the country in generations."

The Shelter chief executive, Campbell Robb, said the cap would drive thousands of people from their homes into areas with more limited job opportunities. A senior London housing official, speaking off the record due to his civil service status, said: " I have been in housing for 30 years and I have never seen anything like this in terms of projected population movements. London is going to be a bit like Paris, with the poor living on the periphery. In many boroughs in inner London in three or four years there will be no poor people living in the private rented sector … it is like something from the 19th century."

The source said: "Given rents in London, in the case of a five-person household living in inner London a family will have £100 a week left to live on, and £60 of that might go on fuel. It is not feasible."

Conservative sources admitted the aim was to push poor, workless families out of inner London and force down rents in the private rented sector – the key driver of the ballooning housing benefit bill.

Tory officials said: "The ultimate effect is that some people will have to move to less expensive areas, but that is fair since if their working peers cannot afford to live in central London, why should a workless family be allowed to remain?" The official added that these workless households could still claim £26,000 a year, the equivalent of £35,000 in taxable income.

The cap will apply to jobseeker's allowance, income support, employment support allowance (the replacement for incapacity benefit), housing benefit and council tax benefit, as well as child tax credit. War widows and those on disability living allowance will be exempt from the cap.

The new upper limit will be delivered by councils through cuts to housing benefit, as this payment is based on a final assessment of a claimant's total income.

A survey by London councils showed 60% of landlords would not lower the rent if the tenant could not pay due to changes in LHA entitlement. If the shortfall in rent rose to more than £20 per week, almost all landlords said they would evict the tenant or not renew the tenancy.

Tenants are then likely to warn councils they are in danger of becoming homeless, and councils will be under a duty to find them temporary accommodation or relocate them to a less expensive property.

There is growing speculation that the Treasury will announce changes to the homelessness legislation in a fortnight, possibly reducing the "local connection" rule that requires councils to house homeless applicant if they have a connection to the area. This would make it easier to shift unemployed claimants out of London.

The Treasury said councils had told it the housing benefit reforms were "doable". The first wave of reform announced in June is expected to save £1.8bn a year, or 7% of the housing benefit bill. The benefit goes to 4.5 million families, of which about a third live in private rented accommodation.

Councils admit private sector rents are too high, but blame a lack of affordable housing, and point out councils are now planning to cut back further due to the dismantling of the planning system.

Last week the Department for Work and Pensions published research showing the average rent paid by low-income working households (LIWH) was £158 – rising to £217 in London. Rent represents around 35% of LIWH incomes.

Local authorities have ditched plans for 160,000 new homes since the coalition government came to power, according to research from Tetlow King Planning for the National Housing Federation.