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A senior Labour source close to the coalition negotiations has just contacted me to suggest where the 'AV without a referendum' story may have originated.

"The idea of AV without a referendum was proposed to us by the Liberal Democrats," he says.

"It was in their first version of the Labour-Liberal Democrat agreement which they proposed to us. That's how it got on the table."

"But at no point," says my source, "was it ever countenanced that we could do it [AV] without a referendum. There was no enthusiasm about the idea that the Lib Dems put to us. And Gordon Brown was the most adamant of all the people in the room that it couldn't be done. So that was the end of the discussion."

There were two reasons, says my source. First, it would just have been wrong to make such a change without a referendum.

"Nobody thought you could go to the country and say we're now going to have AV without a referendum," the senior Labour figure says.

"Second, there's no way we could have got it through the Parliamentary party. It had been difficult enough to get Labour MPs to agree to AV WITH a referendum, let along without a vote."

"And we made that perfectly clear to Liberal Democrats in the negotiations."

In his recent memoirs Peter Mandelson also reveals that the Lib Dems' negotiator, Danny Alexander tried to get Labour to agree to AV without a referendum. The Lib Dems "worry" says Mandelson, "was that the referendum would be lost because voters might see a Lab-Lib pact as a self-interested stitch-up on both sides, so it might be better to avoid such a test."

But then Mandelson reveals that in a series of meetings between the Sunday and Tuesday, the Liberal Democrats "ended up agreeing with us that we should hold a referendum on the alternative vote system".

My senior Labour source can't explain the mystery of why David Cameron ever thought Labour had offered or agreed to such a proposal.

"Perhaps," my source speculates, "Nick Clegg or the Liberal Democrats simply said to the Tories that they had been discussing the idea with Labour."

Strictly speaking, that was true, of course. But my Labour source insists that at no point did Labour ever give any sign they would agree to the idea.

It's only speculation, but if the source's theory is true it would suggest that the Lib Dems misled the Tories, and that David Cameron and his colleagues failed to press them and failed to check whether Labour really had made such an offer.

It could turn out to be one of the great misunderstandings - or deceptions - of modern British politics.

Watch a special edition of Newsnight about the coalition government on Monday 26 July 2010 at 10.30pm on 成人快手 Two.