Mr Osborne faces a growing cross-party consensus that "Help to Buy 2" should be scaled back, with Vince Cable, the Liberal Democrat business secretary, among those to have called on Mr Osborne to reconsider it because of a "raging housing boom".
The OECD, the economic think-tank representing wealthy nations, has called on the government to consider "tighter access" to Help to Buy to address the risk of "excessive" house price inflation.
UK house prices grew by 9.1 per cent in the past year, according to figures from the Office for National Statistics.
Lord Lamont, a Tory chancellor in the early 1990s, told the Financial Times that Mr Osborne was "well aware of the potential problems" with Help to Buy.
But he said he was "concerned" about the scheme, saying it was not in the public interest for house prices to become even more expensive or for mortgage levels to return to their 2007 peak.
"What will happen is that demand can be increased quickly, through measures like Help to Buy, but supply can only be increased slowly," he said. "My concern is that it will become even harder for young people to buy a home in the future."
Mr Darling, chancellor in Gordon Brown's Labour government, told the FT that successive administrations had presided over "bubble after bubble", which all burst eventually.
"We keep repeating the same mistakes," he said. "Supply of housing is the biggest single thing. Unless supply can be increased substantially, we will exacerbate that situation with schemes like Help to Buy."
The mortgage guarantee gives government backing for buyers with a 5 per cent deposit on both newly built and existing homes worth up to £600,000, and aims to boost mortgage lending to those with small deposits. The Treasury plans to offer £12bn of financial backing over the next three years, supporting £130bn of high LTV lending.
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Lord Lawson, who ran the Treasury under Margaret Thatcher, called on Mr Osborne to end the scheme in London and halve the maximum value of properties bought under the programme from £600,000 to £300,000.
Ed Balls, the Labour shadow chancellor, also wants a cut in the threshold to £400,000.
A fourth former chancellor, Ken Clarke, has told allies that he is sceptical about the impact of the scheme, although he has not voiced these concerns in public.
A Treasury spokesman said: "We're dealing with a very specific issue in addressing a market failure after the financial crisis, which has been about affordability and availability of mortgages."
Since Help to Buy 2 launched last October, only 2,572 house purchases have completed through the scheme – less than one per cent of the almost 370,000 transactions in the period. But mortgage lending and buyers' sentiment have already begun to rise sharply.
The largest concentrations of sales so far have been in Scotland and northern England. House prices in these areas are still well below their levels before the market crashed in 2008, and only began to grow again after the launch of Help To Buy.