Nick Clegg's plan to reform the UK's electoral system was tonight caught in a pincer movement between Conservative backbenchers and elements of the Labour party, who both want to change the date of the referendum and potentially derail it.

The executive of the Tory 1922 backbench committee and the shadow justice secretary, Jack Straw, are laying plans to amend the legislation setting up a referendum on 5 May.

Under Clegg's scheme, voters will be asked whether they want to maintain the first-past-the-post system or abolish it in favour of the alternative vote in which candidates are ranked in order of preference.

The Liberal Democrats' opponents started to lay down the battle lines today after the Guardian revealed that Clegg would announce, on Tuesday, that a referendum will be held on 5 May. The deputy prime minister wants to hold the vote on that date to maximise turnout as voters will be going to the polls in the local elections in England and the elections to the devolved bodies.

Downing Street confirmed that David Cameron would campaign for a no vote. Under the coalition agreement with the Lib Dems, the prime minister pledged the Tories would support legislation enabling a referendum. But he and his party would be free to campaign for a no vote.

Tory MPs have been told by Downing Street that even if the referendum is passed, a general election would not be held under AV until a boundary review is held to decide on the new constituencies. "That is designed to stop the Lib Dems walking out of the coalition the day after a yes vote and triggering a general election," one Conservative said.

The executive of the 1922 committee is making elaborate plans to disrupt the referendum. Bernard Jenkin, the former frontbencher who has been appointed to negotiate with ministers, said Tories were duty bound to support the enabling legislation. But he warned that backbenchers would be prepared to table rebel amendments if ministers did not give ground on the date and raise the threshold to make it more difficult to win a yes.

"I am astonished to hear that they are thinking of putting this referendum on the same date as the elections in the Scottish and Welsh parliament," he said yesterday.

Jenkin told the Guardian he would demand a high threshold, possibly modelled on the system used for the Scottish devolution referendum in 1979. A majority of voters (51.6%) supported a Scottish parliament but the referendum was annulled because the rules required a yes from at least 40% of the overall electorate.

Straw said he would support a referendum on AV because Labour pledged to hold one in its general election manifesto. But he told Radio 4's The World at One: "There is an issue about the date. We have got to think about this."

Straw also criticised Clegg's plans to announce at the same time that the Commons would be shrunk by 10% to ensure that parliamentary constituencies are of equal size. This was a key Tory manifesto pledge.

"What would be wholly wrong and quite unprincipled was for the Conservatives with, astonishingly, Liberal Democrat support to use this legislation to slip in these proposed changes which they say are just about equalising boundaries," Straw said.

Clegg will be hoping for more support from the next Labour leader. Ed Miliband, one of the frontunners, said he would campaign for a yes vote on AV "whenever the referendum takes place".