The battle to win the Glenrothes by-election goes into its last lap today, with Labour appearing more pessimistic about the outcome, while the Scottish Nationalists believe that victory may be within their grasp.

Although neither party would make any outright prediction about the outcome of the contest tomorrow, senior Labour sources told The Times they feared that despite making big inroads into the SNP lead in the constituency in recent weeks, they would still fall short of overhauling the Nationalists.

Although on paper the SNP needs to overturn the 10,664 Labour majority gained at the 2005 general election, the corresponding seat was won by the SNP, with a majority of 1,100, at the Scottish Parliament election last year. The Nationalists became the largest party on the local council in 2007.

If Labour does lose, it will seriously dent Gordon Brown's recent “bounce” and rob the Prime Minister of a final flourish to his recent political comeback. It would also mean that Labour had lost a seat that is adjacent to Mr Brown's own constituency of Kirkcaldy & Cowdenbeath.

Another SNP victory, on top of the stunning win at the Glasgow East by-election in July, would mean that Alex Salmond, the First Minister, and his party could claim to be maintaining their popularity despite being in devolved government in Scotland for 18 months. Mr Brown has visited the constituency twice during the campaign and Sarah, his wife, has visited at least six times, almost taking up permanent residence in the constituency in the hope of adding to her husband's recent political revival. Several Cabinet ministers, including Alistair Darling, the Chancellor, have also visited.

Labour will hope that a last-minute trip to Glenrothes today by John Prescott, the former deputy Prime Minister and a renowned campaigner, can turn the tide for them while

Mr Salmond is today expected to visit the constituency for the eleventh time in an effort to maintain the Nationalist momentum.

Labour MPs who spent time in the constituency in recent days say that, while the party should win the majority of votes in outlying parts of the seat, where the mining tradition is still strong, they believe that the SNP enjoys more backing in the town of Glenrothes, where more than half of the 40,000 electorate live.

One senior Scottish Labour MP told The Times: “We are getting a lot of ‘don't knows' on the doorstep when we ask people in Glenrothes itself who they're voting for. That could mean that they are voting Nationalist but don't want to tell us that. The same kind of thing happened in Glasgow East.

“I think there is a fair degree of appreciation of Gordon Brown because he is from these parts, but a lot of people made the jump last year and voted SNP.”

The bookmakers appear to agree with that assessment. Ladbrokes said the SNP's odds had shortened further to 8-15 while Labour's had lengthened to 11-8. On Monday the odds for the SNP were 8-13, with Labour at 5-4. William Hill said Labour had drifted out from 5-6 to 13-8, while the odds on an SNP win had shortened from 5-6 to 4-9. SNP strategists believe that the decision to send 1,200 party activists into the constituency last weekend may prove a masterstroke. “Labour just cannot match that level of activity and campaigning, and we think it could be decisive. At this stage it's vital to have as high a profile as you can.”

Labour yesterday continued its assault on recent changes in home care charges imposed by the SNP-led Fife local authority, with Harriet Harman, the deputy leader, saying after meeting local pensioners, that the new charges were “unfair and unjust”.

Labour also attempted to play on anti-Tory feeling in the constituency by renewing its claim that an SNP victory would be a boost to David Cameron, the Tory leader.

Ms Harman told one interviewer: “Obviously the SNP won't form the next government, so we don't want any satisfaction delivered to David Cameron with the result here.”

Unlike Mr Salmond, who has twice confidently predicted a Nationalist win, Ms Harman restricted herself to saying that the result was “too close to call”.

Lindsay Roy, the Labour candidate, received a boost, however, when he attracted the public support of Ian Rankin, the crime novelist, who comes from Cardenden in the constituency.

The SNP again focused on the impact of high fuel bills, convinced that there is widespread anger in the constituency at recent rises in gas and electricity prices and that the Labour Government is being blamed.

Peter Grant, the SNP candidate, said: “The people of Glenrothes can use their vote to keep Fife moving forwards and to demand action on energy prices to bring down fuel bills this winter.”

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