Cabinet ministers last night set Gordon Brown a two-month deadline to win back voters’ trust or face a full-scale ministerial revolt.

Labour, reeling from defeat in the Glasgow East by-election, plunged into further disarray as MPs and union leaders called for a leadership challenge. Senior ministers lined up to blame the loss of the party’s 25th safest seat on rises in the cost of living. In private, however, a number are preparing to confront Mr Brown this autumn if Labour’s poll ratings do not improve to at least 30 per cent.

One Cabinet minister told The Times that Jack Straw, the Justice Secretary, would be asked to tell Mr Brown to go. If he refused, others were prepared to lead the coup. Another said that it would be miraculous if the Prime Minister were to win back enough support to avoid a challenge later this year.

Labour’s current poll rating averages 26 per cent. Professor John Curtis, of Strathclyde University, an election and poll expert, said that engineering a return to 30 per cent in two months was, while not impossible, the minimum requirement. “No party has come back from below 30 per cent to win the next election,” he said.

A ComRes poll published last night finds only 24 per cent of voters intending to vote Labour, 22 points behind the Conservatives on 46 per cent.

Mr Brown made a barely concealed plea for time as he opened Labour’s national policy forum in Warwick. He repeatedly used the phrase “24 months” – a little over the maximum he has left before he must call an election – as he urged activists not to allow the Conservatives to return to power.

Glasgow East, lost to the SNP on a 22 per cent swing, is the latest and heaviest blow in an electoral pummelling in which Labour has lost 331 council seats, the London mayoralty and the Crewe & Nantwich by-election in the past three months.

Paul Kenny, the general secretary of the GMB union, said that Mr Brown should submit himself to a leadership election to end the uncertainty over his position. “There’s no point dressing it up; it was an unmitigated disaster,” he said. “The MPs have got to make a strong decision as to whether they want to go into an election with Gordon Brown or have a contest.”

The Labour MP Graham Stringer said that the Cabinet should have an “honest discussion” with Mr Brown. “We need a new start and that can only come from a debate around the leadership,” he said.

Calls for a challenge came against the backdrop of clashes between ministers and union leaders at the three-day Warwick meeting to decide Labour’s future policies. Negotiations over the use of the private sector in public services were deadlocked last night and John Hutton, the Business Secretary, provoked fury by questioning the right of union leaders to influence policy.

The dwindling of individual donors willing to bankroll the party has left Labour, in dire financial straits, more dependent than ever on union funding. Efforts to attract wealthy new backers have had little success as evidence mounts that the party is heading for election defeat.

The timing of the by-election at the start of the summer recess prevents an immediate challenge but it also provides Labour MPs with weeks to reflect on their position. Higher than usual turnouts in the Glasgow East and Crewe & Nantwich by-elections indicate that voters are increasingly motivated to bloody the party’s nose. One of those plotting to remove Mr Brown said: “It suits our purposes to have this fester for a month.”

Labour whips have been asked by No 10 to take regular soundings before the party’s annual conference begins on September 20 in Manchester. They are reporting that possible candidates to replace Mr Brown, who include David Miliband, James Pur-nell, Alan Johnson and Jon Cruddas, are already being wooed by MPs.

The Prime Minister intends to reassert his authority with a Cabinet reshuffle after he returns from his holiday. Allies of Mr Brown said that there had been similar threats of a Cabinet-led coup after the May local elections that had come to naught. Downing Street is also playing on concerns that a change of leadership this autumn would require a general election by the middle of next year at the latest.

David Cameron called for an autumn election. “I think the Prime Minister should have his holiday but then I think we need an election. I think we need change in this country and that’s how change should come about,” the Tory leader said.

Alistair Darling led a phalanx of senior ministers who took to the air-waves to insist Mr Brown was still the man to lead the party. “I believe Gordon Brown is the best Prime Minister, the best leader of our party,” the Chancellor told Radio 4’s World at One.

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