The Prime Minister has decided not to campaign in the Glasgow East by-election even though the result could decide his political future, The Times has learnt.

Gordon Brown has opted to abide by the convention that prime ministers do not take a direct part in by-election campaigns, government sources have confirmed.

The convention has been flouted only once in recent years, when Tony Blair visited Uxbridge during a by-election in July 1997. David Cameron, the Conservative leader, has already let it be known that he intends to campaign in Glasgow East, possibly as early as next week.

Mr Brown's decision not to visit the heartlands constituency where Labour had a 13,507 majority in 2005 led to accusations from the Scottish National Party last night that the Prime Minister was “running away from the electorate”.

The decision will be viewed with some disappointment by Labour activists, who are desperate to avoid a tartan version of the Crewe & Nantwich vote in May when Labour tumbled to a humiliating defeat at the hands of the Conservatives.

While Labour insiders in the constituency emphasised last night that they had not really expected Mr Brown to break the long-standing convention, others agreed that a visit by the him would have helped, given that Labour could struggle to hold on to the seat in the face of a strong challenge from the SNP.

One party source said “We need all the help we can get and a visit from Gordon would have buoyed everyone up. It would have sent a message that Labour cares about the people here, and it's a shame he feels he can't come.”

If Labour were to lose the seat to the SNP at the poll on July 24, it is widely thought that it would provoke a crisis of confidence in the Prime Minister among MPs and the party, less than two years from a general election.

With support for Labour haemorrhaging throughout the UK and Mr Brown himself hitting a new low in popularity with every passing opinion poll, the Nationalists believe that they can deliver what could be a fatal political blow to the Prime Minister.

The SNP last night said that Mr Brown was “dodging the fray”. Angus Robertson, the SNP leader at Westminster, said: “Alex Salmond will be there promoting the excellent record of the Scottish government, and I challenge [Mr] Brown to change his mind and try to defend Labour's appalling record in Glasgow East.”

A measure of Labour's apprehension came yesterday, when members of the Shadow Cabinet at Holyrood left after their weekly meeting to campaign in the constituency - even though the party's candidate will not be selected until tomorrow night.

Potential candidates for the Labour leadership in Scotland, vacated at the weekend by Wendy Alexander, also agreed to take a vow of silence about their prospects for the job until the by-election is over.

As reported in The Times yesterday, the leadership campaign will be postponed until after the by-election, with no nominations for the job until the week beginning July 28. It means that the new leader may not be in place until mid-September.

Confirmation that Glasgow East is also already shooting up the political agenda at Westminster came when Mr Brown used Prime Minister's Questions in the Commons to deliver a rebuke to the SNP administration at Holyrood over a claimed cut in funding for the Science Centre in Glasgow.

In answer to a question from Mohammed Sarwar, the Labour MP for Glasgow Central, who said the viability of the centre was now under threat, Mr Brown said: “It's unfortunate in Glasgow that as a result of the SNP, funding has been cut and they will live to regret that.”

Labour and the SNP were involved in an early by-election scuffle after Mr Robertson, the SNP MP for Moray, claimed that Labour had presided over a situation where male life expectancy in parts of Glasgow East was lower, at 63, than in the Gaza strip.

Bob Winter, Glasgow's Lord Provost, said: “To compare the east end of Glasgow to the Gaza strip is just shallow political posturing and insulting to the people of Glasgow East.”

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