LONDON — Around 40,000 British families could be made homeless by welfare cuts introduced by the coalition government, the office of a senior minister has reportedly warned Prime Minister David Cameron.

A leaked letter published in The Observer newspaper on Sunday voices concerns over plans to cap the benefits at £500 (552 euros, $803) a week per family, saying it could leave many unable to pay their rent.

Written to Cameron's Downing Street office by Nico Hislop, the private secretary of Communities Secretary Eric Pickles, it warns the cap risks "disproportionately impacting on families and therefore children".

"Our modelling indicates that we could see an additional 20,000 homelessness acceptances as a result of the total benefit cap. This (is) on top of the 20,000 additional acceptances already anticipated as a result of other changes to housing benefit," says the letter.

The extra costs of dealing with homeless families would outweigh the £270 million a year saved by the cuts, Hislop writes, warning meanwhile of the "level of controversy that this would generate".

Downing Street and the ministry both downplayed reports of a rift.

"They (the Communities Ministry) are supportive of all the government policies on benefits and the need for reforming these areas," a Downing Street spokeswoman told AFP.

A Communities and Local Government spokesman added: "We are fully supportive of all the government's policies on benefits. Clearly action is needed to tackle the housing benefit bill which had spiralled to £21 billion a year."

A government source said the letter had been sent near the start of the year.

Since the Conservative-Liberal Democrat coalition took office in May 2010 it has since announced radical budget cuts in an attempt to slash Britain's record deficit by 2015.