Local authorities in London are preparing to send thousands of homeless families to live in temporary homes outside the capital, in defiance of ministerial demands that people should continue to be housed locally.

Councils are acquiring properties in Kent, Essex, Hertfordshire, Berkshire, Sussex and further afield to cope with an expected surge in numbers of vulnerable families presenting as homeless as a result of welfare cuts from next April.

They say rising rents in London coupled with the introduction next April of stringent benefit caps leave them in an impossible position, with no option but to initiate an outflow of poorer families from the capital by placing homeless households in cheaper areas, often many miles from their home borough. Draft guidance issued by ministers in May says councils must "as far as is reasonably practicable" offer accommodation for homeless families within the borough.

This was ordered by the then housing minister, Grant Shapps, after reports that Newham council planned to relocate households to Stoke-on-Trent, a proposal Shapps, now Conservative party chairman, described as "unfair and wrong".

Guardian research shows London councils have acquired rental properties in Luton, Northampton, Broxbourne, Gravesend, Dartford, Slough, Windsor, Margate, Hastings, Epping Forest, Thurrock and Basildon, and are considering accommodation as far away as Manchester, Hull, Derby, Nottingham, Birmingham and Merthyr Tydfil in south Wales.

Councils said the move was inevitable because there was virtually no suitable private rented temporary accommodation for larger families in London that was affordable within government-imposed housing benefit allowances, which are capped at £400 a week.

"It is going to be practically impossible to provide affordable accommodation to meet our homelessness duties in London," said Ken Jones, director of housing and strategy at Barking and Dagenham council, east London. "As the pressures increase we will be looking to procure well out of London, and even out of the home counties."

All but four of the 33 London local authorities responded to the Guardian survey. Seventeen said they were already placing homeless families outside the capital, or had secured or were considering temporary accommodation outside London for future use. These included Kensington and Chelsea, which has moved a minority of homeless families to Manchester and Slough; Waltham Forest, which has acquired housing in Luton, Margate and Harlow; Brent, which has relocated some households to Hastings; and Tower Hamlets, which has relocated a handful of families to Northampton.

Councils expect a wave of legal challenges from homeless residents who will cite government guidance to argue that their offer of accommodation outside the capital is "unsuitable" because of the impact on their health or their children's education, according to a new study published by the charity Child Poverty Action Group (CPAG) and Lasa.

The CPAG report warns that thousands of homeless families already placed in expensive temporary accommodation in the capital face being uprooted for a second time. Councils could face the choice of picking up the bill for the rent shortfall for these households – expected to run to tens of millions of pounds a year – or moving the families to cheaper homes outside the capital.

Alison Garnham, CPAG chief executive, said: "Families are facing the impossible situation of being told to move to cheaper accommodation that just doesn't exist with London's rising rents. London boroughs are staring at a black hole in their budgets as a result, with costs transferred from central to local government.

"There's still time for government to do the sensible thing and think again when these reforms are debated in parliament before thousands of London's families find themselves uprooted, overcrowded and thrown into turmoil."

MPs are expected to debate regulations that will set detail how the benefit cap will work at a Commons legislation committee meeting on Tuesday.

Government guidance states: "Homeless households may not always be able to stay in their previous neighbourhoods. However, the government considers that it is not acceptable for local authorities to make compulsory placements automatically hundreds of miles away, without having proper regard for the disruption this may cause to those households."

The CPAG report, based on detailed interviews with 11 London local authorities, also found many working households would also face substantial income shortfalls as a result of housing benefit caps. Councils say families are reluctant to move if this would disrupt their children's schooling or cut them off from relatives and friends, causing fears of a surge in overcrowding as families improvise by sharing properties or trade down to smaller flats.

Although it had been anticipated that affordable private rents in expensive inner city areas such as Westminster would be scarce, the acute housing shortage in the capital means market rents outstrip benefit cap levels in cheaper outer London boroughs including Haringey, Waltham Forest, and Barking and Dagenham.

Families have already begun to move from inner London to outer boroughs, with more expected from this month as transitional support for families affected by the housing benefit caps runs out. The government had hoped the housing benefit reforms would force landlords to reduce rents to within cap limits.

But councils say the demand for private rented property from tenants priced out of the housing market means most landlords see no reason to drop rents, and a substantial number say they will no longer consider renting to people who are claiming housing benefit.

Some councils have estimated that up to a third of families affected by the introduction of the £26,000 benefit cap, the local housing allowance cap and under-occupation penalties, known as the "spare room tax", will lose about £100 a week. They face the options of finding more income, moving into cheaper accommodation or presenting to the local authority as homeless. Most authorities have attempted to identify and advise residents at risk of losing income as a result of welfare changes. But there is acceptance among officials that many of the families affected will have few options.

One cabinet member for housing in an inner city borough said: "Let's face it, a lot of people with more than two or three children, and who are dependent on benefits in this borough are not going to be here for very much longer."

Although ministers have introduced a £165m discretionary housing fund for London councils in 2013-14 to help families who can make a special case for staying, the CPAG report says this is inadequate and amounts to less than 10% of the shortfall in benefit income caused by changes.

Councils say some of the households that will be hit by the benefit cap have also been identified by them as needing support under the "troubled families" scheme. But they fear a public backlash if they prioritise them for discretionary housing payments because this would signal that "problematic behaviour was being rewarded".

A government spokesperson said: "It is neither acceptable, fair nor necessary for local authorities to place families far away from their area. The law is already clear that local authorities must secure accommodation within their own borough so far as reasonably practicable, and new rules will reinforce this.

"Our reforms restore fairness to a system that was allowed to spiral out of control under the previous government. It's not right that some families living on benefits should be able to live in areas of London that hard-working families could simply never afford to stay in."

Additional research by Irene Baque

• This article was amended on 15 October 2012. The original incorrectly quoted Hackney council as saying it was "reluctantly looking to procure accommodation outside London" for homeless families. Hackney council says it has no plans to secure accommodation outside London.