LONDON (Reuters) - A senior MP in Britain's ruling Conservative Party said on Thursday she was withdrawing her support for a campaign to leave the European Union over its "shameful" argument that an exit would boost funding for health.

In a blow to the "Out" campaign, which has been gaining in polls before a referendum on EU membership on June 23, lawmaker Sarah Wollaston said leaders of Vote Leave had "knowingly placed a financial lie at the heart of their campaign".

She was referring to the 350 million pounds ($506.42 million) Vote Leave says Britain pays to the EU every week - a figure that has been challenged by the "In" campaign and other economists for not taking into account Britain's rebate.

Vote Leave says it will use some of that money to invest in the country's stretched public health service, the NHS.

Writing in the Times newspaper, Wollaston said: "The claims about health from the Leave campaign have been shameful."

"They have knowingly placed a financial lie at the heart of their campaign, even emblazoning it on their battle bus, alongside the NHS branding, to imply a financial bonanza. It's an empty promise," said Wollaston, who is also a doctor and chair of the parliament's health committee.

With two weeks to go until the referendum both sides of the debate are stepping up their campaigns to win over undecided voters as polls show that Britons are all but evenly split over EU membership.

Wollaston said the campaign had been "unnecessarily acrimonious and divisive" - a charge echoed by several members of Prime Minister David Cameron's Conservative Party, which is deeply divided over Britain's EU membership.

The defense secretary to former Prime Minister Margaret Thatcher, Sir John Nott, suspended his Conservative Party membership, saying on Thursday that Cameron and his finance minister George Osborne had "poisoned the debate" with their "frenetic" warnings of what would happen if Britain left the EU.

The Telegraph newspaper reported that Nott had written in a letter that he would not renew his membership of the party "until we have a change in leadership".

($1 = 0.6911 pounds)

(Reporting by Freya Berry, editing by Elizabeth Piper)