It may have been only a momentary loss of balance, but Gordon Brown’s stumble as he approached the stage seemed to sum up his enfeebled premiership: even putting one foot in front of the other is now fraught with risk.

It was Friday and he was about to give Labour’s national policy forum in Warwick his response to the catastrophic overnight news that the party had lost the Glasgow East by-election.

This was his chance to show he was still fit to be leader. He spoke without notes - David Cameron-style - pacing the stage, firing out gobbets of ideas about the global economy, public services and Labour history in a staccato style.

He failed. As the air-conditioning system lost the battle with the humid July weather, uncomfortable delegates began looking at their watches.

“Have confidence that not only do we have the right policies, but that when the time comes we will be able to persuade the British people,” Brown insisted desperately.

In better days, a Brown speech to the Labour faithful might have been punctured by a dozen standing ovations. This half-hour address received just one ripple of applause before the end. And that was only after Tom Watson, a burly Cabinet Office minister, stood up and ostentatiously began clapping, forcing the rest to follow.

“The usual stuff, wasn’t it?” grumbled one delegate afterwards as she cooled down with an ice cream. “Lots of stuff about global economics when what everyone cares about is what’s happening in our shopping baskets. He totally misses the point - it was as if last night never happened.”

The Glasgow defeat, which saw Labour lose a super-safe 13,500 majority to the Scottish National party in a 22% swing, was the worst the party has suffered in modern history.

In the London mayoral race, the Crewe & Nantwich and Henley by-elections, and now Glasgow, Labour has been humiliated in virtually every kind of political terrain. Almost no Labour MP can be certain of returning to Westminster after the next general election.

The fear among friends of the prime minister is that he risks political oblivion unless he wakes up to the grave and imminent threat to his leadership.

Ministers believe a formal challenge is likely, perhaps inevitable, when politics resumes in September after the August break. “Things are finely poised,” said one. “We are in a very dangerous period indeed. We cannot be sure which way things will go.”

Yesterday, speculation of a coup against Brown mounted. Senior Labour figures telephoned, e-mailed and texted each other pondering what to do with the “Gordon problem”.

Even seasoned loyalists accept the party is in a dark place. Hazel Blears, the communities secretary, said: “When your party is in a tough way you have a choice: tear each other apart or pull together - and it is vital we do exactly that.”

Pulling together seems, however, to be beyond Labour’s ability any more.

LABOUR strategists always knew the Glasgow East by-election would be tough, but until the morning of the poll, few had actually expected to be defeated. The bookmakers took more than £100,000 in bets on Labour winning, including, it is rumoured, some from the party’s own campaign team.

The received wisdom was that it was a predominantly Catholic seat and Glaswegian Catholics always voted Labour. However, these loyalties no longer have such a powerful pull.

Labour paid the price for taking its voters for granted, too. Its campaign fixers, led by Motherwell’s bruiser MP Frank Roy, were shocked to discover that the outgoing MP, David Marshall, had no data on local voters. As a Labour rotten borough for almost a century, there had been no need.

There were other factors: the economic gloom, the chaos in the Scottish Labour party following the resignation of its leader Wendy Alexander, and, of course, the personal unpopularity of Brown even in his Scottish homeland. “It was payback time,” said one local member.

Brownite loyalists insisted the result was not disastrous, pointing out that Labour also suffered local electoral setbacks under Tony Blair but won three general elections in a row.

Professor Michael Thrasher of Plymouth University’s Elections Centre disagreed. “However much voters hated the government then, they were prepared to give Labour the benefit of the doubt because of the economy,” he said. “That is no longer the case. And Tony Blair, unlike Gordon Brown, was a proven election winner.”

Labour’s tiredness and absence of ideas after 11 years in office were also weighing on the party, he added.

Brown’s critics within the party remain tireless, however, particularly in their calls for a lurch to the left to save Labour.

“We need not just a new regime, a new leader, but a new party that favours us - our people,” Michael Meacher, the former environment minister, said yesterday in his first public call for Brown to quit.

“We have got to come up with some policies on housing and taxation and equality. If [Brown] can’t do it, someone else has got to. It has got to be this year if it happens, because then we are facing just 12-15 months with a new leader before an election. How much evidence do you want? The evidence is staring us in the face.”

There was insurrection, too, among the grassroots. The semiofficial Labourhome.org website was flooded with angry calls for Brown to step aside.

“If any business, football team or any organisation had a string of results like ours, you look to the person in charge and ask what is to be done,” posted one member. “‘It’s the economy’ and ‘I’m getting on with the job’ are not accountable answers and I think we have a right to demand better.”

There were also rumblings deep within the normally acquiescent parliamentary party. Patrick Hall, the moderate Labour MP for Bedford, expressed the anxieties of dozens of parliamentary colleagues.

Glasgow East was “a serious loss”, he said. “If the situation hasn’t changed by this winter we’ll have to think about changing the leadership. Personal loyalty is important, But in politics, ultimately the party has got to come first.”

For months, Westminster has been rife with fanciful plots against the leadership. Now the malcontents are drawing up precise game plans and time-tables. One of Brown’s leading Blairite critics explained how a coup might work.

“There is no point in doing anything in August because so few people are in the country,” he said. “MPs will be spending time with their families and constituents and reflecting on the gravity of the situation. September is the month when things will happen.”

The plotters will pin their hopes initially on the so-called “greybeards” of the cabinet, led by Geoff Hoon, the chief whip, and Jack Straw, the justice secretary. Last night friends of Hoon said he would remain loyal to Brown. Straw’s aides also insist he remains steadfast – although yesterday he disappeared for his summer holiday in the United States without making a postGlasgow public pledge of loyalty. MPs claimed Straw’s allies were running a covert “charm offensive” on his behalf with a view to a leadership campaign if Brown goes. The backbench plan to topple Brown could run like this. On Monday September 1, the coup leaders would make contact with the greybeards and warn them that they had a week to persuade Brown to go gracefully.

One plan being actively discussed at the highest reaches is the so-called “death with dignity” strategy. Brown would be offered a senior international post, probably in the area of international development, as a way of sugar-coating his exit from Downing Street.

“Gordon is head and shoulders above anybody else on the world stage,” said a cabinet source. “Does he want to continue with the humiliation he routinely suffers in the domestic arena? Nobody wants to humiliate anybody else.”

Brown remains passionate about the United Nations’ millennium development goals to improve health and education in Africa. One senior government figure suggested a high-ranking UN position could be found for him to oversee the plan’s completion. “No vacancy exists at the moment,” said the source. “But Gordon is sufficiently respected overseas, it would not be hard to get a job for him created.” If the greybeards failed toper-suade Brown to quit with dignity, the plot would move to stage two. During the week beginning September 8, junior ministers and parliamentary aides would join the assault. The plotters hope for a string of resignations, coupled with demands for Brown to go. Former cabinet ministers would also call for regime change.

Trade union leaders gathering in Brighton for their annual congress would play a role, too. At Warwick on Friday, Paul Kenny, the general secretary of the GMB, called for Brown to face a leadership challenge. By September other “brothers” will have come round to his way of thinking, the plotters hope.

If the coup went according to plan, Brown would be given the opportunity of an emotional farewell speech at Labour’s conference in Manchester, starting on September 20. This would then become a forum for leadership contenders to say how to rebuild the party.

The principal candidates would be Straw, David Miliband, the 43-year-old foreign secretary, and the health secretary Alan Johnson. Ed Balls, the schools secretary, would try to put together a campaign. James Purnell, the 38-year-old work and pensions secretary, would not be ruled out. And Harriet Harman, the deputy party leader, is also said to be considering a bid.

BROWN himself, of course, has other ideas for the September political “grid”. He begins his summer holiday in Suffolk this week; and he will be using the time to plot his autumn fightback, with new policies, personnel and political style. His task is to persuade sceptical and fearful colleagues that he can discover a winning streak.

There will be a package of economic reforms aimed at kick-starting the stalled housing market, and addressing concerns about the price of fuel and food. One idea is to provide extra benefits to the poor and elderly this winter to cope with soaring heating costs. Meanwhile, magpie-like, he is searching every government department for shiny policies that might be stolen for his all-important conference speech.

A new post of Whitehall co-ordinator or “minister for the Today programme” is set to be created in an attempt to give the administration structure and coherence. Shaun Woodward, the Northern Ireland secretary and former Conservative MP, is expected to get the job.

“Shaun was communications director to John Major in the run-up to the 1992 election,” said one MP. “In those days the Tories were suffering defeat after defeat in by-elections, but Major bounced back. Gordon finds that analogy comforting and Shaun has become an increasingly important figure in Team Brown.”

Nobody in Downing Street is saying “relaunch” to describe the fightback, but that is what it will be. Brown’s aides, led by Stephen Carter, his senior adviser, are trying to help him to develop a less buttoned-up and more empathetic public style. That was the thinking behind his speech in Warwick on Friday. However flawed it might have been, and however uncomfortable he was without notes or a podium, this is the “new” Brown.

As he strolled through the Downing Street rose garden with Barack Obama yesterday, Brown must have been hoping that some of the presidential candidate’s stardust might rub off on him.

It is sometimes hard to pin down what makes one politician a success as a leader and another a loser. Not in this case.

Obama networked as a young man as hard as Brown did to build his political career, yet he has created the illusion of transcending politics. Brown remains mired in politics when the public has no taste for it. As one Labour blogger noted woundingly yesterday, he is “a workhorse not a leader”.

Who would be left to lead Labour after a Glasgow-style swing?

If Glasgow East’s 22.5% swing against Labour were repeated at a general election, Gordon Brown would lose his Kirkcaldy seat.

Who would get the job of leading the ragged collection of two-dozen-odd MPs that would make up the postelection Labour rump? Harriet Harman, come on down.

The MP for Camberwell and Peckham, Labour’s 15th safest seat, would have to slug it out with the remaining handful of former ministers. Yvette Cooper, the Treasury chief secretary, would survive but not her husband Ed Balls. So would Andy Burnham, the culture secretary.

Might David Blunkett, whose Sheffield Brightside seat is the fourth safest, fancy his chances of a political comeback? Or could this be the big moment of the MP for Birkenhead Frank Field?

The lessons of history suggest that the days after a resounding defeat are perfect for launching a leadership bid. When trounced in 1931, Labour was left with just 46 MPs. Arthur Henderson, the party leader, lost his seat, leaving George Lansbury and Clement Attlee as the only senior figures on the Labour benches. Lansbury took over the leadership, Attlee became his deputy. Four years later Lansbury resigned, Attlee took over and led Labour for the next 20 years.

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