Brexit defector Dr Sarah Wollaston has told Sky News that Vote Leave knew its £350m NHS claim was "untrue" but dismissed her concerns by saying it "gets people talking".
The Conservative MP and health select committee chair said she repeatedly told senior Leave colleagues that it was a lie to suggest Brexit would mean an extra £350m a week for the NHS.
But she said they refused to correct it and she was told that "it didn't really matter".
As a result, she said, she refused to hand out leaflets or get on board the Vote Leave battle bus with it emblazoned on the side.
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Dr Wollaston, who announced she was dropping her support for Leave in favour of Remain, told Sky News: "I believe they know it is not true. The argument that’s sometimes made to me by those within the campaign is that it doesn't really matter because it gets people talking about the numbers.
"Well I came into political campaigning for honest data in public life so I am afraid I made it clear right from the start I couldn't hand out their leaflets or step on board a battle bus where there was something that simply wasn't true right at the heart of their message."
She added: "The trouble with having as the centre of your message a figure that is fundamentally untrue and that I believe they knew to be untrue, it then undermines the rest of your argument."
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Leave campaigner Nadine Dorries MP said the high-profile defection of such a well-respected Conservative MP was a "deliberately staged and political" move "coordinated by Number 10".
Others suggested she had been persuaded by the prospect of a role in the Department of Health in any post-EU referendum reshuffle.
But Dr Wollaston told Sky News she had "neither asked for nor been offered" a promotion.
Former communities secretary and 'In' campaigner Sir Eric Pickles said others were likely to follow Dr Wollaston out of the Brexit exit and cross to the Remain campaign.
A Vote Leave spokesman described her decision as "bizarre" and added: "Given her views on the EU in the past it is disappointing to suddenly see her repeating lines straight from the Remain campaign hymn sheet."
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He said: "From day one we have been clear that we hand Brussels £350m and we get some of that money back - but we don't have control over it. We think that it is best to have control over our money.
"We are sorry Sarah doesn't want to spend more money on the NHS but that's been our message from day one."
Former cabinet minister Grant Shapps also came out for Remain on Thursday but said he had "not been impressed" by the campaigning on either side.
Sky's Political Editor Faisal Islam tackled Mr Gove on the £350m claim when he appeared on the In or Out programme, saying the amount the UK paid to Brussels was not that high because of the rebate - which means that figure is reduced. In addition, projects in the UK get funding from the EU.
The Leave campaign has also been pulled up on its initial claim the £350m would go to the NHS - and have revised it down more recently to say £100m would be spent on the NHS.
Despite Dr Wollaston's defection, the Leave camp has been able to celebrate a couple of victories of its own.
Former Tory cabinet minister Sir John Nott suspended his party membership in protest against the "tirade of fear" he says has been put out by Mr Cameron's Stronger in Europe campaign, according to The Daily Telegraph.
JCB chairman Lord Bamford, meanwhile, has written a letter to his 6,000 workers explaining why he is supporting Brexit.