Sarah Woolaston, the Conservative MP for Totnes and formerly a GP, left Vote Leave because she said it was making claims about the amount Britain could spend on the NHS which were "untrue".
Specifically she was referring to Vote Leave's claim that £350m extra could be spent on the NHS each week if Britain left the EU.
"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," she told the BBC.
Her departure has been labelled as a significant blow for Vote Leave, given her knowledge of the NHS as a former GP.
Daniel May-Miller from Christians on the Left has said that Vote Leave has got its maths wrong, however Sir Gerald Howarth, a Christian Conservative MP and Out campaigner, has said that Sarah Woolaston has "misunderstood" the point that Out campaigners are trying to make.
Speaking on Premier Christian Radio Daniel May-Miller said: "Almost everyone is disputing that big 350 million pound figure - that's the total amount of money we send to the EU before any of the money that we get back.
"By then saying 350 million - we could give that to the NHS - well we couldn't, because a whole load of that money is already spent."
Speaking on Premier's News Hour, Sir Gerald Howarth said: "She [Sarah Woolaston] has misunderstood the position. Of that 350 million, 175 million is spent by the EU on other countries - completely outside our control.
"If we left the European Union we would have 175 million pounds a week... to spend on our priorities."
Listen to Premier's Aaron James speaking to Daniel May-Miller:
Listen to Premier's Hannah Tooley speaking to Sir Gerald Howarth on the News Hour: