Attempts by Labour to avoid a heavy defeat in the Crewe & Nantwich by-election are being undermined by bitter wrangling over attempts to brand the Conservative candidate a “toff”.

An inquest is already under way into Labour's campaign, as a series of opinion polls suggest that David Cameron is on course to inflict a fresh electoral humiliation on Mr Brown this Thursday.

Ministers, MPs and even senior figures in No10 are preparing to blame the invocation of class war if, as expected, they lose the seat held until her death by Gwyneth Dunwoody with a 7,078 majority. Her daughter, Tamsin, a former Welsh Assembly member, is fighting to keep the seat for Labour.

The party has branded Edward Timpson, her Tory opponent, a “Tarporley Toff” in reference to a well-heeled Cheshire village outside Crewe and Mr Cameron has been followed by the party's activists in top-hats and tails on his visits. Embarrassment was added to Labour unease yesterday when it emerged that one of those mocking Mr Cameron's class had himself attended a fee-paying school.

Harriet Harman, the Leader of the House of Commons, admitted that Labour's campaign was “not the most positive”, as the first public signs of recrimination began to emerge. Ed Miliband, the Cabinet Office Minister, also distanced himself during interviews from the campaign stunts. Mr Brown is thought to have personally authorised the use of class as a campaign issue despite the reservations of a number of senior ministers and advisers. Stephen Carter, the new strategy chief at No10, is reported to be among those who urged Labour not to attack the Tories on class grounds.

Nor will Mr Brown find much support among backbenchers if the party loses badly. Jon Cruddas, an influential critic on the Left, told The Times recently that Labour was making a mistake in seeking to caricature Mr Cameron and his closest allies as “posh boys” and he is likely to repeat the criticism later this week.

The Labour campaign in Crewe is being run by Steve McCabe, MP for Birmingham Hall Green. He has insisted privately that the focus on Mr Timpson's background is proving effective in rallying core voters.

Two opinion polls at the week underlined Mr Brown's task. A YouGov poll for The Sunday Times put the Tories on 45 per cent to Labour's 25 per cent, with the Lib Dems on 18 per cent, up two points since last month.

A second constituency poll, conducted by ICM for the News of the World, suggested that 45 per cent of constituents were planning to vote Conservative and 37 per cent Labour.

David Davis, the Shadow Home Secretary, said that the Tories were pulling out all the stops to win and predicted that the party would go on to win a general election. Mr Cameron is expected to make his third and final visit to Crewe today as both main parties flood the constituency with MPs and activists. One of the few senior politicians who will not be seen in Crewe is Mr Brown himself. By convention prime ministers do not make campaign visits to constituencies before by-elections.

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