David Cameron has been warned by one of his most trusted cabinet ministers that his welfare policies risk making 40,000 families homeless.

The extraordinary claim, in a letter to the prime minister from the office of Eric Pickles, the communities secretary, exposes deep splits at the heart of government over plans to cap benefit at £500 a week per family.

The letter, leaked to the Observer, reveals Pickles's belief that the cap – announced with great fanfare at last year's Tory conference – will increase the burden on taxpayers, because thousands of families will be unable to pay their rent and will have to seek local government help. It blows apart the government's public insistence that a limit on benefit payments will have little impact on homelessness and child poverty.

Written by Nico Heslop, Pickles's private secretary, at the clear instigation of the minister, the letter lays bare fears of mass homelessness "disproportionately impacting on families". It says:

■ 40,000 families will be made homeless by the welfare reforms, putting further strain on services already "seeing increased pressures".

■ An estimated £270m saving from the benefits cap will be wiped out by the need to divert resources to help the newly homeless and is likely to "generate a net cost".

■ Half of the 56,000 affordable homes the government expects to be constructed by 2015 will not be built because developers will realise they will not be able to recoup even 80% of market rates from tenants.

The leak is the first time that disagreements over welfare cuts have surfaced within the Tory high command.

Liam Byrne, the shadow work and pensions secretary, said the letter suggested ministers had not come clean over the effects of their policy. "We were assured by ministers that costs wouldn't rise. Now top-level leaks reveal the truth. Iain Duncan Smith has promised the House of Commons he will not U-turn on the benefits cap. Perhaps now David Cameron will order him to think again."

Jenny Willott, the Liberal Democrat welfare spokeswoman who has already warned that a rigid cap would increase child poverty, said she remained "very worried" about the proposals, which are due to come into effect in 2013.

Last month, employment minister Chris Grayling rebuffed an attempt by Labour to protect those facing homelessness from the benefit cap. Dismissing a Labour amendment to the welfare reform bill, he said: "It is not yet clear to what extent they would be affected by the overall benefit cap."

The bill has since passed to the Lords, although the revelations will only fuel existing concerns among Liberal Democrat and Labour peers.

Labour MP Karen Buck, who sits on the Commons committee, said Pickles's letter proved there was confusion and division at the centre of government. "The housing department and the benefits department are pursuing policies which don't just cut across, but actively undermine, each other," she said.

Campbell Robb, chief executive of Shelter, the charity for the homeless, said: "With 21% of people struggling to meet housing costs, it's naive to think you can cut support without putting some people at risk of losing their home. The coalition government should stop bulldozing through badly thought-through policies while ignoring independent evidence, its own expert panel and the views of those who will deal with the very real impact on people."

Enver Solomon, policy director at the Children's Society, said: "The social costs of the cap are huge and would have disastrous consequences for many children."

The leaking of the letter will be a source of considerable embarrassment to the government.

It was sent by Heslop to Cameron's private secretary, Matthew Style – the normal channel of communication used by cabinet ministers for formal matters of policy.

Over two pages, the fears of the Department for Communities and Local Government (DCLG) are spelled out over "some very serious practical issues for DCLG priorities".

The letter says: "Our modelling indicates that we could see an additional 20,000 homelessness acceptances as a result of the total benefit cap. This on top of the 20,000 additional acceptances already anticipated as a result of other changes to the housing benefit. We are already seeing increased pressures on the homelessness services."

It adds: "We are concerned that the savings from this measure, currently estimated at £270m [per year] from 2014-2015, does not take account of the additional costs to local authorities (through homelessness and temporary accommodation). In fact we think it is likely that the policy as it stands will generate a net cost."

The letter then claims that with the reduction in the benefit families can claim, developers will not be able to recoup anything close to a market rent and so will not have an incentive to build homes. "Initial analysis suggests that of the 56,000 new affordable rent units up to 23,000 could be lost," the letter says. "And reductions would disproprortionately affect family homes rather than small flats."

Of a proposed policy that families would be required to divert part of the general benefits, such as child benefit, to cover housing costs, it adds: "It is important not to underestimate the level of controversy that this would generate."

A spokesman for Pickles said: "We are fully supportive of all the government's policies on benefits. Clearly action is needed to tackle the housing benefit bill which has spiralled to £21bn a year under Labour."