Gordon Brown's authority as Prime Minister was dealt a severe blow today, as Communities Secretary Hazel Blears quit the Cabinet on the eve of crucial European and local elections.

Conservative leader David Cameron said the fourth ministerial resignation in two days showed the Prime Minister had lost command of a Government which was "collapsing before our eyes", while Liberal Democrat leader Nick Clegg told MPs: "Labour is finished."

But Mr Brown rejected opposition calls for an immediate General Election, insisting he was focusing on cleaning up the parliamentary expenses system and helping Britain through the recession.

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However, he ducked Mr Cameron's challenge to say whether Alistair Darling - tipped for the chop in the reshuffle expected within the next few days - would still be in the Treasury next week.

In a letter to Mr Brown confirming her resignation, Ms Blears said she was proud of her service to the Government over the past eight years and would "work tirelessly to see Labour elected at the next General Election".

But she pointedly offered none of the usual expressions of support for the Prime Minister or his policies.

In response, Mr Brown praised the Salford MP's achievements as a minister and said he hoped she would return to Government in the future.

Downing Street said Ms Blears, who told the PM she was going in a face-to-face meeting today, would be replaced as Communities Secretary "very shortly".

Meanwhile, rumours swept Westminster of an email campaign by rebel Labour MPs seeking backbench signatures for a letter urging Mr Brown to stand down as leader, which could be delivered on Monday if the party receives the expected drubbing in tomorrow's elections.

One former minister said there was "huge" desire in the party for a change of leadership, but MPs were waiting to see whether a "heavyweight" challenger would come forward.

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Another backbencher suggested there could be an impromptu vote of no confidence in the Prime Minister when the Parliamentary Labour Party meets on Monday.

And senior backbencher Barry Sheerman warned Mr Brown was "in trouble" if he did not react swiftly to widespread disillusionment in the PLP.

The Guardian website said some Labour rebels believe they can persuade up to 80 MPs to sign a demand for his resignation. Earlier reports said thy had drawn up a timetable for his removal by the first week of July. But several key allies this afternoon stepped forward with unequivocal support for the Prime Minister, which some commentators said should give him a little breathing space.

The BBC reported that it had seen a copy of the letter but its political correspondent Iain Watson said he understood some backbenchers would be happy to sign any anti-Brown letter, but others who have criticised the PM would refuse to sign because they believed bringing forward a general election would be "catastrophic".

Ms Blears' resignation came less than two hours before Prime Minister's Questions in the House of Commons and followed announcements yesterday from Home Secretary Jacqui Smith, children's minister Beverley Hughes and Cabinet Office minister Tom Watson that they would leave Government at the reshuffle.

In a statement, Ms Blears said she wanted to return to grassroots activism, adding: "I never sought high office for the sake of it, or for what I can gain, but for what I can achieve for the people I represent and serve."

In a comment seen by some as an indication she believes the Brown administration has lost touch with voters, she said she wanted to "help the Labour Party to reconnect with the British people".

A former party chairman and one of the most prominent Cabinet Blairites, Ms Blears had come under increasing pressure over her expenses after Mr Brown said it was "totally unacceptable" for her to avoid paying capital gains tax on the sale of a property for which she had claimed the parliamentary second homes allowance.

Some saw the PM's comment - which came after she repaid more than £13,000 to HM Revenue and Customs - as revenge for her earlier mockery of his appearance on YouTube.

In a stormy PMQs, Mr Cameron told Mr Brown the decision of the minister responsible for local government to step down the day before council elections was "a direct challenge to his authority".

Britain now had "a dysfunctional Cabinet, a dysfunctional Government, led by a Prime Minister who can't give a lead" and needed an immediate General Election, the Tory leader said.

And Mr Clegg told MPs: "We can now see the Government is in total meltdown. The Prime Minister is thrashing around, fighting for his own political survival.

"The country doesn't have a Government, it has a void. Labour is finished. The only choice now is between the Conservatives and the Liberal Democrats."

The Prime Minister sought to brush off the attacks, paying tribute to both Ms Blears and Ms Smith and accusing the Tory leader of ducking policy issues.

"At a time like this the House should come together to acknowledge contributions that have been made in the public interest," he said.

"We have got two jobs of work to do. One is to clean up the expenses system, where I think everyone in this House except (Mr Cameron) agrees that we have got to take action now to clean up the system. The other is the recession."

Speaking after PMQs, Business Secretary Lord Mandelson said Mr Brown and the whole Government faced "a challenge ... to keep our nerve at a time when we have got to go through a genuine crisis in our politics".

Cabinet ministers Andy Burnham and Hilary Benn also took to the airwaves to insist Mr Brown should remain as Prime Minister.

And Jim Sheridan, chairman of Westminster's group of Scottish Labour MPs, called for "cool heads", telling the BBC: "This party has to stick together, we need discipline, and I think Gordon is the man to instil that discipline in people."

But the normally loyal Mr Sheerman warned: "I think that, if the Prime Minister doesn't realise that, across the party, there is a disillusionment with the way the parliamentary party has been consulted, treated and valued, he is heading for trouble.

"If you lose your base of support, and if even the Cabinet starts to feel unhappy with the leadership of the Prime Minister, then that is one indication of unhappiness and destabilises a regime.

"If you do that with a broader group of colleagues in the parliamentary party, right across the political spectrum, then you are really in trouble and you've got to do something fast before it gets unstoppable."

Former home secretary John Reid tonight issued a statement through his office insisting that he would not be returning to government.

However his office refused to comment on a report that Mr Reid had turned down an offer of his old job at a meeting last night with Mr Brown.

The brief statement said only: "John Reid will not be returning to government. Any reports to the contrary are untrue."

Meanwhile Health Secretary Alan Johnson, who is seen as Mr Brown's most likely successor, said the Prime Minister was still the best man for the job.

"He is doing the job and there is absolutely no-one who could do the job better," he told Sky News.

Asked if he could personally do a better job than Mr Brown, Mr Johnson replied: "No".