Olympics minister Tessa Jowell and London Mayor Ken Livingstone say that they will be able to recoup £1.8bn following the Games from land sales at the Olympic site in east London.

But reports claim a London Development Agency warns that, if land prices increase by 6% annually over the coming years, it may be possible to raise only £800m.

Some of the cash from land sales is intended to go the National Lottery to repay loans used to fund the Games and to ensure that other lottery-funded good causes do not lose out. Any shortfall in that money could hit heritage, sports and arts projects.

The report came as MPs prepared to approve the use of lottery funds to support the Games in a House of Commons vote on the Olympic Lottery Distribution Fund Order.

A spokesman for the Department for Culture, Media and Sport denied it had over-estimated the amount of money that could be raised in a post-Olympics land sale.

The £800m figure was simply the lowest in a range of projections in the LDA report, which suggested that as much as £3bn could be raised if market conditions were favourable, he said.

The spokesman said: "There is absolutely no black hole in the 2012 finances, and these claims are completely misleading and a distortion of the facts.

"The £800m quoted is the most cautious of a range of LDA projections of how much might be raised by land sales in the Olympic Park, based on 6% per annum growth.

"This is significantly less than the average rate of increase over the last 20 years - a period that has included both economic highs and lows."