Labour was today hoping against hope that it had done enough to defend the constituency of Glenrothes, as voters went to the polls in a by-election situated squarely in the Prime Minister's backyard.

The vote was triggered by the death of sitting Labour MP John MacDougall, who had a majority of 10,000 in the seat, which lies next door to Gordon Brown's Kirkaldy and Cowdenbeath constituency in Fife.

Dramatic falls in voter confidence in Labour have made this once unassailable majority look vulnerable to attack by the Scottish National Party.

The SNP overturned a bigger deficit to win Glasgow East earlier this summer. The nationalists' hopes of repeating the feat in Glenrothes today remain strong, although they have been dented by a resurgence of support for Mr Brown because of his sure handling of the economic crisis.

Scotland’s First Minister Alex Salmond, the SNP leader, has visited the constituency more than 10 times and is confident his party can pull off another shock.

Mr Brown too has twice travelled to the constituency, making it the first by-election he has campaigned in since becoming Prime Minister - a sign of Labour's growing optimism in recent weeks that Glenrothes can be salvaged.

Mr Brown's wife Sarah has spent much of the last two weeks knocking on doors to canvass support in the seat.

A procession of big Labour beasts has also headed to Glenrothes, including John Prescott, the former Deputy Prime Minister, and Alistair Darling, the Chancellor of the Exchequer, whose seat lies nearby in Edinburgh.

Lindsay Roy, the Labour candidate, is the head teacher of Mr Brown’s former school and cast his vote this morning at a local primary school alongside his wife, Irene.

“I am confident, optimistic, but not complacent," he said as he left.

“We need to get our vote out. I think we have a very good chance of winning. I think eventually we will be at the front when the poll is counted.”

Peter Grant, who is standing for the Nationalists, is the leader of the local Fife council. After casting his vote at the Collydean Primary School, he said: “The signs are we are going to win.

“There’s still a lot to be done. We have a fantastic team of volunteers out now making sure everyone who has promised us their vote will deliver that.

“If they do, as I think they will do, we will be the ones that are celebrating this evening.”

The Tory and Liberal Democrat leaders, David Cameron and Nick Clegg, have also travelled to Glenrothes in support of their candidates.

Lib Dem candidate Harry Wills has campaigned for a 2p cut in income tax to help hard-pressed families, while Tory Maurice Golden says a vote for him will send a “message of change” to Mr Brown.

The most recent Parliamentary by-election in Fife saw the Liberal Democrats capture Dunfermline and West Fife in 2006, overturning a Labour majority of more than 11,000.

Mr Salmond and the Scottish Labour leader Iain Gray today traded verbal blows at First Minister’s Questions, each trying to gain political advantage on the subject of council cuts in the Fife region where Glenrothes is situated.

The grumpy exchange took on a personal edge when Mr Gray told MSPs: “I have to say the First Minister is no Barack Obama.”

This drew the retort from Mr Salmond: “It‘s certainly true I‘m no Barack Obama. The problem for Iain Gray is, he is no Jack McConnell (the smooth-tongued former leader of Scottish Labour).”

Times Recommends

• Milk: do we need a dairy godmother?
• DIY: the women doing it for themselves
• First double portrait of Princes unveiled