Tories have 'no chance' of winning by-election says Cable

But he denied suggestions the Conservative Party was holding back in the contest to give its coalition partner a better chance of victory.

Prime Minister David Cameron fuelled suspicions of a deal last week when he wished Elwyn Watkins, the Lib Dem candidate in the January 13 poll, well and said he hoped for a "friendly" campaign.

Mr Watkins missed out on the seat by just 103 votes in May but the result was declared void last month by an election court which found that victorious Labour candidate Phil Woolas had made false statements about him.

Although Mr Watkins is Labour's nearest challenger, the constituency was a three-way marginal in May, with Conservative Kashif Ali – who is standing again – less than 2,500 votes behind.

But asked about the Prime Minister's intervention, Mr Cable said it was a "straight fight" between his party and Labour.

"We have not got his support. He is putting up his own candidate and people can compete. But I think people in Oldham can do the arithmetic and can see that this is a straight fight between the Liberal Democrats and Labour and they can make their calculations on that basis."

Labour has selected Debbie Abrahams as its candidate.

The by-election is being seen as an indicator of how the two

parties in the coalition Government will behave when pitched against one another in the fight for votes.

Mr Cameron has confirmed he will visit the constituency to campaign for Mr Ali and insisted Tories would be "fighting for all the votes" but he then took the unusual step of saying he wished the Lib Dems well in the by-election because of Mr Watkins's experiences during the general election campaign.