Nearly two-thirds of voters are open to changing the system

Poll shows momentum growing for the alternative vote campaign, even among Tory supporters

The battle to overhaul Britain's voting system is wide open, with almost two-thirds of people amenable to ditching first past the post.

An exclusive poll for The Independent on Sunday says a third (34 per cent) have already decided to back the alternative vote in the referendum planned for 5 May, a vote which Labour peers are seeking to delay.

But the ComRes survey reveals 61 per cent could be persuaded to support changing the voting system when they have heard more of the arguments for and against. Surprisingly, 54 per cent of Conservative voters are open to persuasion.

It comes as the Labour leader, Ed Miliband, said he would honour his pledge to campaign in favour of AV. "The reason politics is discredited is because politicians always break their promises," he said. In a speech to a Fabian Society, he also made a direct appeal to Liberal Democrats unhappy at their party's "tragic mistake" in joining the Tories in government.

But the overtures were quickly dismissed by senior Lib Dems, with Nick Clegg understood to be privately furious at the way some of Mr Miliband's colleagues in the Lords are blocking the path to electoral reform. "For a man supposedly in favour of AV, he's got a funny way of showing it," said a source close to the Deputy Prime Minister. "If Ed Miliband really is part of the new politics he professes to be, then he really needs to get a grip on his lords and stop them putting petty political point-scoring ahead of fixing our broken political system."

The Parliamentary Voting System and Constituencies Bill needs to become law by 16 February for the poll to be held on 5 May. Three extra days of debate are planned for this week, with peers facing being forced to sit through the night to head off an attempt by Labour peers, including John Reid, to derail the legislation.

Some Lib Dem peers have proposed splitting the Bill to fast track the AV element. A separate Bill dealing with the Tory policy to reduce the number of MPs by 50 and redraw every constituency boundary would follow later in the year – something Conservatives insist is "unthinkable".

An increasingly confident Yes camp wrote yesterday to Margaret Beckett, the former foreign secretary who is president of the No to AV campaign, demanding she put forward "truthful and honest arguments" in favour of first past the post.

Jonathan Bartley, spokesman for Yes to Fairer Votes, challenged Mrs Beckett to a public debate. "We will, of course, give you the time to try to come up with a logical, consistent and coherent argument," he said.

Matthew Elliott, campaign director of No to AV, has insisted: "We know that most people simply don't want to change to a more unfair, complicated and expensive voting system."

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