Much as I hate to oppose a tax cut, in the case of stamp duty on house sales it is necessary to make an exception. Yesterday, various rumours were doing the rounds: one version has it that the Government will allow homebuyers to defer the payment of stamp duty, another that the tax will be suspended altogether in an attempt to stimulate the housing market.

Invited to comment on the Today programme, the Chancellor, Alistair Darling, certainly didn't deny the Government was considering these options - from which it is safe to deduce that this is yet one more case of the Government floating a proposal through a controlled leak, then analysing the reaction before committing itself to action. It isn't hard to see why the Government is desperate to revive the housing market. Gordon Brown is acutely sensitive to the role played by house prices in the mood of voters.

When house price inflation was at its peak in 2003, he changed the Government's preferred measure of inflation from the retail prices index, which includes an element of house prices, to the consumer prices index, which excludes all housing costs. The effect was to move the goalposts for the Bank of England, keeping interest rates lower than they otherwise would have been and allowing the boom to continue. Whenever the housing boom appeared to be flagging thereafter, he pumped money into shared equity schemes, adding to inflationary pressures in the housing market.

Now that the boom is over, the Government has been fishing around for ways of trying to arrest the collapse. In April, Mr Darling attempted to persuade the banks to increase mortgage lending by swapping £50 billion of mortgages for government bonds - effectively transferring risk to the taxpayer. In the event, the mortgage-for-bonds swap proved a miserable failure. The banks said thank you very much - and then carried on tightening their lending criteria and raising their fixed rates.

If the Government thinks it can buck the housing market by granting homebuyers a temporary reprieve on stamp duty, it is doomed to a second miserable failure. How can I judge this? Because it is what happened when Norman Lamont, the Conservative Chancellor, introduced a stamp duty holiday in the depths of the last housing crash in December 1991. Housing transactions slumped from 1.306 million in 1991 to 1.136 million in 1992, which remains the lowest figure recorded in the past 30 years. Prices, according to the Nationwide, carried on falling, by 2.6 per cent during the eight months in which stamp duty was suspended.

In August 1992 Anthony Nelson, then Economic Secretary to the Treasury, announced the end of the holiday, saying it had cost the public purse £400 million at a time of rising debt. “In the longer term,” he said, “it is the reduction of interest rates that will bring about the firmest and surest revival of the property market.” In this, he was quite right: the beginning of the end of the last housing slump began a month later, on Black Wednesday, when the Government stopped trying to peg the pound to the mark and interest rates fell as a result.

A stamp duty holiday this time around will cost far more than £400 million. In 2006-07, stamp duty on sales of residential property raised £6.5 billion. Even without a stamp duty holiday this will fall by more than half in the current fiscal year because the number of house sales has plummeted. At the same time, the Government's borrowing requirement is soaring as recession eats away at tax revenues. In the Budget, the Chancellor predicted a public sector net borrowing requirement of £43 billion for the year 2008-09. Yet in June alone he had to borrow £9.25 billion. Now, with the economy flagging, would be a great time to reduce taxes - if the Government had the money. But it doesn't, because of its irresponsible spending spree during the good years.

Why try to pump up the housing market anyway? House prices are falling because they reached absurd heights: even after an 8 per cent fall over the past 12 months they are trading at around seven times average earnings. When banks were keen to lend mortgages of six times a borrower's salary, these prices were just about affordable. Now that banks have reverted to more traditional lending practices - a decade ago most were prepared to lend a maximum of three times a borrower's earnings - there is a huge gap between asking prices and what buyers can actually afford. Freeing buyers from having to pay stamp duty - which is levied at rates varying from 1 per cent on a £125,000 home and 4 per cent on a £500,000 property - will make scant difference in a market that is still probably overvalued by a third.

There is just one effect that the Government will have achieved by leaking the suggestion of a stamp duty holiday: the few people who are in a position to buy will now be tempted to put off their purchases until the Government makes a proper announcement on stamp duty, perhaps in September. Expect house sales figures for August to be the gloomiest yet.

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