Gordon Brown's move to back more tax-raising powers for Holyrood was calculated to meet growing anger in England about the funding advantages enjoyed by Scotland, The Times has learnt.

Senior Westminster sources said that the Prime Minister is increasingly concerned that voters in England see devolution giving Scots more spending per head and allowing them to enjoy policies unavailable in England such as free care for the elderly, free university education and cheaper NHS prescriptions.

The sources added that while Mr Brown reluctantly accepted the argument that the Scottish Parliament has to be more accountable for its spending, his U-turn was also aimed at calming English irritation.

“This answers both problems. You show the Scots you are listening and you also act to show you're not ignoring the growing English stone in the Prime Ministerial shoe,” a government minister said.

At present the Scottish government receives a £30billion annual grant from the UK Treasury. If Holyrood was allowed to raise more of its own cash, the amount which has to be transferred in the block grant and the importance of the controversial Barnett Formula, which gives Scotland a share of any new public spending in England, would diminish. That would allow Mr Brown to argue in England that he has acted to cut funding to his native Scotland, while also appearing to accede to Scottish demands for more devolved powers.

In his speech on Thursday in Glasgow, in which he unveiled his U-turn on devolution's remit, he said that he was committed to strengthening the Union, which is now under almost constant attack on both sides of the Border. Mr Brown spoke of the “problem” created by devolution in that Holyrood was not responsible for the size of its budget.

Westminster sources dismissed claims yesterday by the SNP that the Prime Minister was “caving in” to pressure from them since they took power at Holyrood last year.

“Actually, this has been a problem since before the SNP took power. People were already addressing the question of why politicians in Edinburgh, of whatever party, should be handed £30billion to spend as they liked without having to worry about raising it,” a source said. “It is simply untenable. The question of financial accountability would still have been there even if the Nationalists had not won last year.”

Mr Brown carried out private engagements in Glenrothes yesterday — a sure sign of his anxiety about the forthcoming by-election. There is growing speculation that if Labour loses, Mr Brown will face renewed calls from within his party to stand down as Prime Minister.

The widespread opinion among economists in Scotland was that greater fiscal authority for Holyrood would act as an incentive to Scottish politicians to improve the economy because Holyrood would keep any revenues raised.

John Swinney, the SNP Finance Secretary, said Mr Brown's change on devolution was “massive” after last year saying that there was no case for more powers for the Scottish Parliament. “Here we are a year later, Gordon Brown has caved in to pressure from the Scottish National Party and rising support for the SNP, based on the aspirations of the people of this country,” he added.

“I'm immensely encouraged that we are now going to be in a situation where we will have a Scottish Parliament ... that will have more financial powers. That will make us better able to make Scotland a more successful country.”

Mr Swinney also signalled that even if Holyrood acquires more financial muscle, it would neither slow the SNP's drive for independence nor its argument for control of North Sea oil revenues.

An official commission headed by Sir Kenneth Calman and set up jointly by Labour, the Conservatives and the Liberal Democrats is studying whether Holyrood should be given greater powers, although independence has been excluded from its remit.

Tavish Scott, the Lib Dem leader at Holyrood, called on Mr Brown to back up his talk with action. “The people of Scotland will judge him harshly if these turn out to be weasel words just to get through a difficult by-election.”

Annabel Goldie, the Scottish Tory leader, said that Labour was in an “irretrievable mess” and that David Cameron, the UK leader of the Conservatives, had shown his respect for devolution and Holyrood. “He seeks a positive and constructive relationship with the Scottish government, whatever its political hue. That is the real way forward for 21st century Scotland and Britain,” Ms Goldie added.

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