Senior members of the Campaign Group of Labour MPs have privately begun discussing whether to try to force a leadership contest at next year's party conference.
A challenger would first require the backing of 20 per cent of Labour MPs - currently 71 of the 355 elected at the May general election. A call for a contest would then have to be approved at the annual conference on a card vote.
One Labour MP said: "We've already got around 36 names. It's possible if there is a mood change in the party that we could get enough. Blair's decision to defy Gordon Brown and stay on could change things."
Left-wingers were already discussing a plan to oppose Gordon Brown when the Prime Minister stands down. Some have suggested Michael Meacher, the former environment minister, who has told friends he believes there should be a contest.
Other names under discussion are Alan Simpson, a leading member of the Campaign Group, and Frank Dobson, the former health secretary, who is passionately opposed to Mr Blair's health reforms.
Now left-wingers are discussing a plan to speed up their challenge after Mr Blair made clear in his Labour conference speech on Tuesday that he wants to remain in Downing Street until 2008.
Bob Marshall-Andrews, a Labour MP and QC and critic of Mr Blair's anti-terror legislation, said: "The Prime Minister has invited the Parliamentary Labour Party (PLP) to consider the question of the succession and we have now a responsibility to look at the options for a leadership contest."
Although a left-wing candidate would stand little or no chance of defeating Mr Blair, a challenge could destabilise his leadership.
In 1989, Margaret Thatcher was wounded by a stalking horse challenge by the late Sir Anthony Meyer. It paved the way for a more serious challenge by Michael Heseltine the following year which led to her resignation.
Mr Brown would not be a party to any moves to run against Mr Blair next year, but some of his supporters may be tempted to support a rebel candidate in an attempt to loosen Mr Blair's grip on power.
Yesterday Mr Blair refused to give a timescale for his departure from Downing Street in a series of media interviews to mark the close of Labour's Brighton conference.
In a coded warning to Mr Brown's supporters, he said people would expect Labour to get on with the job of running the country. He said the public did not want "endless debates" about the leadership issue. "What the country wants to know from me - we have just won another election - is 'what are you going to do for us?'."
In the closing speech to the conference, John Reid, the Defence Secretary and a Blairite, warned that faction-fighting by rival camps could destroy Labour.
He said: "Factions have never been the saving grace of the Labour Party. They have always been our destruction. If the priority of the Government is 'education, education, education', then the priority of the Labour party is 'unity, unity, unity'."
Left-wing MPs are ready to oppose a series of reforms to health and education after Mr Blair this week made clear his determination to drive them through before he stands down.
In the event of a leadership election, it would be decided by an electoral college in which trade unions, MPs and constituency parties each have a third of the votes.
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