More than a half of Labour supporters believe that Gordon Brown should stand down to make way for a more electable alternative.

Today’s Populus poll for The Times — the first survey since last Thursday’s local elections — shows a dramatic collapse of confidence in Mr Brown’s leadership.

The Prime Minister’s personal rating has dropped sharply, along with that for Labour. He now trails David Cameron and Nick Clegg in the leadership stakes.

Labour lost the London mayoralty and 331 council seats in Thursday’s rout. Labour MPs returned to Westminster in despair, fearing another setback in the Crewe & Nantwich by-election on May 22, which Mr Cameron has decided to make a test of his credibility.

A huge factor was the abolition of the 10p tax rate. Backbenchers have demanded that Alistair Darling, the Chancellor, announce quickly how he intends to compensate low-paid workers who are worse off.

Frank Field and Greg Pope, who are leading the backbench campaign, met Mr Darling. In a statement last night, they said that they were told that he was searching actively for as many losers as possible and considering how they could be compensated.

Mr Brown was subjected to more criticism. Charles Clarke, the former Home Secretary, called on him to dispense with “dog whistle” slogans, such as his “British jobs for British workers”.

The most devastating finding of the poll is that 55 per cent of Labour voters believe that the party would be more likely to win the next general election if Mr Brown resigned “to make way for a younger, fresher, more charismatic alternative”.

Mr Brown’s leader rating (on a 0 to 10 scale) has dropped sharply from 4.50 to 4.08 in a month — well below the other leaders. His rating among those saying that they will vote Labour at the next election has fallen to 5.68 (from 6.26 in April and 6.72 in March). Among people who voted Labour in 2005, Mr Brown’s rating is now 5.04, down from 5.60 in April.

Other key findings from the poll, taken between May 2 and 4, include:

— Support for Labour has fallen by four points in a month to 29 per cent. The Tories have gained one point to 40 per cent; their lead of 11 points is the largest in the five years of Populus polls. The Liberal Democrats are two points up at 19 per cent, with other parties one point ahead at 12 per cent.

— The number who trust Mr Brown and Alistair Darling most to deal with economic problems has fallen to 30 per cent, down from 43 per cent in mid-March and 61 per cent in early September.

— The poll suggested that Mr Brown could not solve his problems by bringing in fresh faces with a big Cabinet reshuffle. Only 36 per cent think a reshuffle would make Labour more likely to win the next election. Only Labour voters, by a 51 to 41 per cent margin, support a reshuffle.

— More than two thirds of all voters, and nearly four fifths of Labour supporters, think that significant policy changes in areas such as the NHS, crime and tax would make Labour more likely to win the next election.

Mr Field said that the Chancellor’s failure to explain properly the compensation deal for those affected by the abolition of the 10p tax rate, had damaged Labour. He gave warning that the issue would continue to harm the party until it was dealt with fully.

Mr Cameron has decided to make the 10p row the centrepiece of his Crewe campaign. “We’ve got 15 days to overturn Labour’s majority of more than 7,000,” he said, before heading off to the constituency. “Obviously it’s going to be a tall order but we are going to give it our best shot. Our message will focus in particular on the 10p tax rate and how Gordon Brown is hurting the people of Crewe with tax increases just at the moment their cost of living is going up.”

Mr Brown presided over a lengthy session of the Cabinet at which there was reported to have been frank exchanges during an inquest about the poll setbacks. While ministers strongly supported Mr Brown, they called for urgent action to show that Labour was, as he insisted in television interviews on Sunday, on the side of working people.

— Populus interviewed a random sample of 1509 adults aged over 18 by telephone between May 2 and 4. Interviews were conducted across the country and have been weighted to be representative of all adults. Populus is a member of the British Polling Council. For more details go to www.populus.co.uk.

Times Recommends

• 'Kelvin MacKenzie ate my paper'
• Cold, dark journeys of the lone wolf
• It’s too easy to blame dads