Tavish Scott, the recently-elected leader of the Scottish Liberal Democrats, yesterday stunned his political opponents by challenging them to support an immediate 2p cut for Scottish taxpayers.

However, Mr Scott's attempt to wrest the initiative towards his party by offering voters a tax windfall of £330 a year began to unravel when he and his aides appeared to be at odds over how much such a cut would cost.

First reports of Mr Scott's policy gamble suggested that he had estimated the annual cost to the Scottish government's £30 billion budget at £400million.

Mr Scott himself did not demur from this figure when it was put to him in a television interview at lunchtime yesterday from his party's national conference at Bournemouth. But within hours, his aides were clarifying matters by saying that it would actually cost £800million a year.

Asked to explain why Mr Scott himself had not corrected the interviewer, a party press officer said: “He was standing in front of the sea in a bad light. And he was short of time.”

Mr Scott wants the Scottish Parliament to implement the 2p cut by invoking the powers granted to it in the Scotland Act to vary the basic rate of income tax by up to 3p in the pound. These powers have not being used in the first nine years of devolution and Mr Scott set out yesterday, in a speech to the party conference, why he thought this should change. He said that the British economy was in meltdown, adding: “People are tightening their belts. It's right that government does as well.”

This was a reference to his preferred method of funding such a cut in tax for Scots - by, for example, scrapping the Scottish Futures Trust set up by the SNP government last week as a replacement for the private finance initiative. However, this would only save £14 million in set-up costs, although his spokesman emphasised that it was an indication of the wider cuts in government that Mr Scott wanted.

He is also proposing that, for the foreseeable future, all additions to the Scottish budget through the Barnett Formula, which gives Scotland a proportion of all new public spending in England, should be used to finance the cut in tax in Scotland.

Mr Scott's call came as Nick Clegg is already floating a tax cut for all British taxpayers of 4p in the pound, funded by increases in green taxes. This would mean that the overall saving for Scottish taxpayers would be 6p in the pound.

In his first conference speech since being elected Scottish leader, Mr Scott said: “Putting money back in the pockets of people who need it most - that is my practical ambition.”

He told delegates that energy costs were up by half, food costs had increased by £30 a month and inflation was at its highest for 16 years.

“We can't let this go on,” Mr Scott said. “We can't turn our backs. We've got to find ways to help people out, because we know things are going to get worse. Where others talk tax up, I want to bring tax down.”

While Mr Scott knows that there is no chance of Holyrood taking such a dramatic step on income tax, he feels that by floating the idea that the party's standing with Scottish voters - about 14 per cent in the polls at the moment - will rise.

The SNP pounced on the confusion over how much the tax measure would cost by saying that Mr Scott had got his sums wrong and claiming that they had been calculated “on the back of a cigarette packet”.

“If these proposals were put forward the Scottish public would face deep spending cuts of up to £800 million a year,” said a source close to Alex Salmond, the First Minister.

Iain Gray, the new Scottish Labour leader, said that with class sizes and home help charges going up, the last thing that vulnerable people in Scotland wanted was more cuts in services.

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