Tory MP Sarah Wollaston has quit the campaign to leave the EU and will vote for Remain instead, she told the BBC.
Dr Wollaston, chairman of the health select committee, said Vote Leave's claim that Brexit would free up £350m a week for the NHS "simply isn't true".
She told the BBC's Laura Kuenssberg that she did not feel "comfortable" being part of the campaign.
Vote Leave has stood by its much-criticised £350m claim, which is on the side of its battle bus.
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But the Totnes MP, who is a GP, said: "For someone like me who has long campaigned for open and honest data in public life I could not have set foot on a battle bus that has at the heart of its campaign a figure that I know to be untrue.
"If you're in a position where you can't hand out a Vote Leave leaflet, you can't be campaigning for that organisation."
'Unfortunate attacks'
Dr Wollaston said she thought there would be a "Brexit penalty" on the NHS because leaving the EU would hit Britain's economy.
"The consensus now is there would be a huge economic shock if we voted to leave," she said. "Undoubtedly, the thing that's most going to influence the financial health of the NHS is the background economy. So I think there would be a Brexit penalty."
Dr Wollaston defended her decision to change camps saying "nobody wants politicians who make the wrong decision" and it would be "far worse" not to change her mind.
Asked if some of her colleagues may also be having second thoughts, Dr Wollaston said: "I'm sure. Any politician who is not prepared to have second thoughts should not be doing the job."
Dr Wollaston said attacks Conservatives had made on each other during the campaign were "really unfortunate".
Image copyright BBC NewsIn February, Dr Wollaston accused Prime Minster David Cameron of "taking voters for fools" for suggesting refugee camps like the "Jungle" in Calais could move to England if the UK left the EU.
Mr Cameron tweeted that her decision to swap sides in the referendum debate was a "powerful intervention".
Vote Leave have been urged to stop using the £350m claim by the UK statistics watchdog and the Treasury select committee but the campaign insists that although Britain gets some of the money back it does not have control over how it is spent.
Leave campaigner Michael Gove urged the government to commit to spend an extra £100m a week on the NHS by 2020 if Britain votes to quit the EU on 23 June.
Meanwhile, in a blow to the Remain campaign, Sir John Nott, Conservative defence minister during the 1982 Falklands War, has suspended his membership of the party because of David Cameron's "tirade of fear" during the EU referendum campaign, according to The Daily Telegraph.
Sir John, who famously stormed out of a live interview with the BBC's Sir Robin Day during the Falklands War, is reported to believe that Mr Cameron and Chancellor George Osborne have "poisoned the debate" with their "frenetic" warnings about the consequences of a Brexit.