The claims, made in a letter to the Prime Minister from the office of Eric Pickles, the communities secretary, expose deep divisions at the heart of the UK government over plans to cap benefits at £500 a week per family.
The letter, seen by Scotland on Sunday, reveals Pickles' belief that the cap will increase the burden on taxpayers, as thousands of families will be unable to pay their rent and be forced to seek local government help.
Concerns raised by Pickles, a former chairman of the Conservative party, are contrary to the coalition government's insistence that a limit on benefit payments will have little impact on homelessness and child poverty.
The letter, written by Nico Heslop, Pickles' private secretary, lays bare fears of mass homelessness "disproportionately impacting on families".
It adds: "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."
Concerns are also raised that the 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".
It also states that 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 senior ranks of the Tory party.
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" he said.
"Now top-level leaks reveal th e 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."
Last month, employment minister Chris Grayling rebuffed an attempt by Labour to protect those facing homelessness from the benefit cap.
The bill has since passed to the Lords, however the revelations will only fuel existing concerns among Liberal Democrat and Labour peers.
Campbell Robb, chief executive of Shelter, the charity for the homeless, said: "With 21 per cent 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.
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