A planned cross-party event involving Ed Miliband and Nick Clegg for the yes to the alternative vote campaign has collapsed as the offices of the two party leaders trade bitter recriminations.

The row reveals just how raw relations have become between the two parties, and comes as the polls start to show that the no campaign is gaining momentum, although it is still behind.

The yes campaign had planned to stage a rally with Charles Kennedy, the former Lib Dem leader, Miliband, and Caroline Lucas, the leader of the Greens, at a London educational institution on Tuesday.

Lib Dem sources say that there were suggestions that Clegg take part, in order to present a united front and to avoid rumours about his absence. They say Labour rejected the idea as they decided late on that Miliband should speak alone.

The two party leaders' offices also discussed the possibility of Clegg speaking, but not while Miliband was on the platform. Labour, they say, rejected this offer too. Labour claims Clegg's office subsequently ordered Kennedy not to attend.

The Lib Dems categorically deny vetoing Kennedy's appearance and instead say they were assured that Miliband intended to make a speech alone, his first on AV. They also said the issue of which Lib Dems would appear had diminished as the event changed format. A senior Lib Dem said: "We are relaxed about whoever wants to appear on a platform. We're not vetoing anyone."

As a result of the spat, the planned event has been cancelled, but discussions are apparently continuing about the possibility of a joint platform before the 5 May referendum.

Miliband will instead go ahead with a separate launch of the Labour yes campaign with Neil Kinnock and Peter Hain on Wednesday, at which he will say he "bows to no one in his disgust at what Clegg is doing in propping up a Tory government". But he will argue that AV is the best chance the progressive majority in Britain has of getting its voices heard.

The Miliband team said the yes campaign had told them that Clegg's involvement would set back their cause. "Nick is not the right poster boy for this campaign. If this is supposed to be beyond party politics, Clegg needs to be nowhere. We are still willing to share a platform with a Liberal Democrat figure like Paddy Ashdown or Kennedy at some point."

It is said that Miliband will not have much more time to campaign for a yes vote as his priority from April will be the Welsh, Scottish and local council elections. The Lib Dems are frustrated by Miliband's attitude, arguing he is playing short-term party politics. They argue that Labour needs to realise that it is unlikely to be allowed to govern alone – and that if the AV referendum is lost, there won't be another chance of electoral reform for 30 years.

In his speech to party members in Sheffield, Clegg claimed the no campaign was desperate. He said reform would end the scandal of safe seats. "If you want more duck houses, vote no. If you want more democracy, vote yes. In seven weeks, the British people can sound the last post for first past the post, so we have seven weeks to get our message across that 'if you want MPs to work harder for your vote, vote yes'.

"On the yes side, we have the Liberal Democrats, Labour party supporters, the Green party, Ukip, Plaid Cymru, the SNP, Friends of the Earth, Colin Firth, Eddie Izzard and Helena Bonham Carter. On the no side are the BNP, the communists, the Conservative party, John Prescott, Norman Tebbit and David Owen."

In his speech to the Labour yes compaign on Wednesday, Miliband will say: "I know this referendum is far harder to win because of Nick Clegg's broken promises. But we can't reduce the second referendum in British political history to the betrayal of one man. Look past Nick Clegg to the chance to change our politics. I supported the inclusion of an AV referendum in our manifesto because I believed the time was ripe for change. If it was right then, it is right now.

"I also say this: the tragedy of British political history for the left has been the split in the progressive parties. For most of the last 100 years, Britain has been a progressive country with a reactionary government. Two progressive parties have split their votes under first past the post and one Conservative party has mopped up a substantial minority.

"Maybe the Liberal Democrats have now taken a historic and decisive turn to ally themselves forever more with the Conservatives.

"More likely, the Clegg era will be seen as an aberration and the danger then is we return to business as usual under first past the post."