Labour is increasingly optimistic that it will be able to see off the SNP challenge and win the Glenrothes by-election on November 6.

Senior Labour sources who have spoken to The Times believe that the party is building a momentum towards victory for Lindsay Roy, the local headmaster who is the party's candidate.

The message coming out privately from Labour insiders is at variance with the public pronouncements of senior ministers. At the weekend only hours after Gordon Brown visited the constituency, Jim Murphy, the Scottish Secretary, insisted that Labour was still the underdog and had ground to make up on the Nationalists.

Yesterday, however, one authoritative source said: “We're finding our vote is very strong and we are optimistic that we have the momentum. It's a totally different feeling from in Glasgow East with ten days to go, when the SNP had the momentum.”

Labour saw its 13,507 majority disappear in Glasgow East, where the SNP won by 365 votes in July. In Glenrothes it is defending a 10,664 majority and the contest, which at one time looked likely to end in another SNP win, has been transformed by Mr Brown's political recovery on the back of his handling of the global financial crisis.

The bookmakers appear to agree with Labour's private assessment. While they still make the SNP favourites at 4-7 on, Labour's odds have shortened from 5-1 against a month ago to 5-4 now.

It appears that the Prime Minister is preparing to make two more visits to the constituency, which borders his own seat of Kirkcaldy and Cowdenbeath, before polling day.

Yesterday, it was the turn of Chancellor Alistair Darling, who used his visit to a college in Methil to repeat the core Labour message that the economic clout of the United Kingdom was crucial to Scotland. “It is only because of the strength of the United Kingdom we were able to put into place measures to increase the capital in the British banking system, including RBS and HBOS,” he said.

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