Labour figures in Scotland are becoming increasingly anxious that the plans to hold a crucial by-election north of the Border on July 24 could undermine the party's vote because the date is in the middle of the traditional Glasgow Fair trades holiday fortnight.

They are pointing out that while Labour is odds-on to hold the Glasgow East seat, many of the party's natural supporters could be on holiday and away from the constituency on the day of the poll.

While Labour has a 13,500 majority in the seat, the by-election battle could be vital for the future of Gordon Brown as Prime Minister. If Labour lost such a heartland Glasgow seat to the Scottish National Party, it could place massive pressure on Mr Brown to quit No 10.

One source said last night that while the traditional Fair Fortnight does not now lead to the exodus from Glasgow it once did, there are still thousands who leave the city for their annual summer holiday.

He added: “It's the kind of seat where the turnout will struggle get above 50 per cent anyway, so Labour needs to make sure that it doesn't shoot itself in the foot by holding the by-election at the worst time possible.”

All the signs are that the Labour Party hierarchy will go ahead with the by-election on July 24, with the local councillor George Ryan the clear favourite to be the Labour candidate.

After recent heavy defeats in the Crewe & Nantwich and Henley by-elections, and the resignation of Wendy Alexander, Labour's Scottish leader, many in the party are nervous about the contest.

David Marshall, the MP for Glasgow East, formally resigned from the Commons yesterday for health reasons.

The 67-year-old Mr Marshall is said to have been suffering from depression, and received advice from two doctors that he should not carry on.

He is a former chairman of the Commons Scottish Affairs Committee and has been MP for Glasgow Shettleston and more recently Glasgow East since 1979.

A party spokesman said last night that it was still deciding when to move the writ that officially sparks the contest.

“The National Executive Committee will consider the timetable in due course but at this time our thoughts are with David Marshall and his family,” he said.

“David has been an outstanding champion for the people of Glasgow all his life and he will be sorely missed.”

The constituency, home to Celtic Football Club, had the highest Labour vote share in Glasgow - 60.7 per cent - at the 2005 general election. The Scottish National Party, buoyed by its Holyrood election successes in 2007, would need a 21.9 per cent swing to snatch the seat.

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