Gordon Brown wants the Glenrothes by-election to be held on November 6, two days after the US presidential election, local party sources have told The Times.

The news emerged as Margaret Beckett told Labour MPs yesterday to get behind the Prime Minister or pay a heavy price at the next election.

Mrs Beckett intervened as Labour's ruling executive prepared today to rebuff demands from rebels for a leadership contest. Westminster was awash with rumours of more ministerial resignations.

Two more rebels, George Howarth and Janet Anderson, explained why they had called for nomination papers. Mr Howarth, MP for Knowsley North, said: “At the moment it seems to me that people, because they think that the Prime Minister is not necessarily the right person to lead the country, have switched off. We've got to get them to switch on again and listen to what's going on. If Gordon can do that, then it's quite possible he could continue as Prime Minister. If he can't, I think the important thing is that we have a contest.”

Ms Anderson, MP for Rossendale & Darwen, writing in the London Evening Standard, said: “What is clear is that we have to do something. We cannot go on ‘sleepwalking into oblivion', but we are - and we will continue to do so if we do nothing to address the reasons why we have been so far behind in the polls. That means a . . . review of our policies and how we communicate them. And if that requires a change of leadership, so be it.”

Mrs Beckett, who was acting leader after John Smith's death in 1994, told the BBC: “The British people will neither understand nor forgive a party that appears to be more concerned with its own internal disputes than with their very real problems.”

Mr Brown will present a paper to Labour's national executive today setting out the Cabinet's thoughts on how to fight the next election. Earlier it was announced that Barry Gardiner, another rebel, had left his position as Mr Brown's special envoy for forestry. The Prime Minister's spokesman insisted that Mr Brown was focused on the big issues. He said: “What the Prime Minister is doing is concentrating on the issues that matter to the country - the situation in the economy, what is happening in the financial markets, Northern Ireland and crime.”

In the Glenrothes by-election, Labour will defend a 10,664 majority against a strong challenge from the SNP.

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