Ed Miliband is joining Labour's Eastleigh by-election campaign with a challenge to the Liberal Democrats to back his plans for a "mansion tax" in a Commons vote.

The Opposition leader is travelling to the Hampshire town where the Lib Dems are engaged in a fierce battle to prevent their Tory coalition partners snatching the seat.

Labour is hoping for a good showing in the contest sparked by the resignation in disgrace of ex-cabinet minister Chris Huhne after he admitted dodging a speeding penalty. But despite recruiting best-selling author and satirist John O'Farrell as its candidate, insiders acknowledge it has no realistic chance of winning on February 28.

Mr Miliband will use his visit in a bid to capitalise on his surprise announcement that Labour favoured reviving the 10p income tax rate. Labour says that could be paid for by a levy on £2 million-plus homes - a policy promised in the last Liberal Democrat manifesto but opposed by the Conservatives.

The party hopes to put the "mansion tax" proposals to a vote either before the Budget in an opposition day debate or through an amendment to the Budget-implementing Finance Bill.

"It's time for Nick Clegg and the Liberal Democrats to be honest with the people of Eastleigh and show whose side are they on," Mr Miliband is expected to say during his visit.

"They must answer this question: will they vote with Labour in advance of the Budget to force David Cameron and George Osborne to act? Or will the Liberal Democrats do what they've done for two-and-a-half years: prop up a Tory Government that is squeezing the living standards of the middle harder and harder?"

Tory backbenchers have been campaigning for the 10p rate to be reintroduced in next month's Budget, and the PM has hinted he was ready to agree. "There could be a majority in the House of Commons when it votes on our proposal. But only if the Liberal Democrats vote with Labour," Mr Miliband will say.

Prime Minister David Cameron and Mr Clegg have already made their first forays to Eastleigh - underlining how high the stakes are for both leaders.

A win for the Conservatives would help to convince restive Tory backbenchers that Mr Cameron still has a chance of leading them to outright victory at the next general election. Equally Mr Clegg needs the Lib Dems to hold the seat if he is to allay fears of a catastrophic collapse the next time the UK goes to the polls.