London councils will be forced to ship thousands of families out of the capital – some as far away as Wales – after next April’s benefits cuts mean they are priced out of the private rental market.

A report by the Child Poverty Action Group and Lasa, a welfare rights charity, predicts that 124,480 London households will be hit by a combination of cuts to Local Housing Allowance, the new benefit cap which means no household can claim more than £26,000 a year in total, and under-occupation penalties.

The report, ‘Between a rock and a hard place: the early impacts of welfare reform on London’, found that many councils are actively considering obtaining accommodation elsewhere, despite the possibility of legal action, while others believe that making up private rent shortfalls will leave the authorities with gaping holes in their budgets.

Alison Garnham, CEO of the Child Poverty Action Group, 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.

“It’s not right that children are left paying the price for London’s housing crisis, which they did nothing to create.”

According to a survey in the Guardian, some London councils are already acquiring properties in Kent, Essex, Hertfordshire, Berkshire and Sussex, and are considering accommodation in Manchester, Hull, Derby, Nottingham, Birmingham and Merthyr Tydfil in South Wales.

This is despite guidance issued by then housing minister Grant Shapps in May telling councils that they must “as far as is reasonably practicable” offer accommodation for homeless families within the borough.

The guidance says: “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.”

Ken Jones, director of housing and Strategy at one council, Barking and Dagenham, said: “It is going to be practically impossible to provide affordable accommodation to meet our homelessness duties in 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 few 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.

Hackney council said it was “reluctantly looking to procure accommodation outside London”.

Local councils in London say that because of buoyant demand, private landlords see no reason to drop rents for benefits tenants, and that many landlords are stopping taking this kind of tenant.