Michael Gove backing Boris Johnson over cash for NHS post-BrexitThe Foreign Secretary is at the United Nations in New York, where he is expected to meet the Prime Minister later this week amid recriminations over his blueprint for a so-called "hard" Brexit.
Downing Street sought to play down the row over the Foreign Secretary's essay, insisting that Mrs May "values" contributions from all members of her Cabinet.
Mr Johnson's 4,000-word article has led to calls for his sacking and prompted Home Secretary Amber Rudd to accuse him of "backseat driving".
It exposed Tory divisions over Brexit before Mrs May's expected offer of a compromise with Brussels in a Friday speech in Florence, Italy.
The Foreign Secretary also revived the controversial claim that £350 million a week of funds would come back under UK control after Brexit - and could be used as a source of extra cash for the NHS.
That resulted in him becoming embroiled in a messy spat with UK Statistics Authority chairman Sir David Norgrove.
Speculation has been mounting that the PM will offer to pay tens of billions of pounds to the EU during a two to three-year transition deal after the UK's formal exit in 2019 in order to break the deadlock in negotiations.
Mr Johnson "accepts the idea of payments of our dues during the transition period" but not payment for access afterwards, a source close to the Foreign Secretary said.
In the Daily Telegraph article that triggered the latest round of Tory infighting, Mr Johnson said: "We would not expect to pay for access to their markets any more than they would expect to pay for access to ours.
"And yes - once we have settled our accounts, we will take back control of roughly £350 million per week. It would be a fine thing, as many of us have pointed out, if a lot of that money went on the NHS."
Environment Secretary Michael Gove, who worked closely with Mr Johnson on the Vote Leave campaign but dramatically fell out with him over the Tory leadership battle, gave his support to the Foreign Secretary.
Amid the row over the £350 million claim, Mr Gove tweeted it was "important people look at what Boris actually wrote" in his article and the "debate should be forward looking on how to make most of life outside EU - not refighting referendum".
Prominent Tory Brexiteer John Redwood said there was no "moral or political or legal reason" to continue paying money to the EU after leaving.
He accused the Treasury of briefing that the UK would be prepared to continue paying into Brussels' coffers.
Although he stopped short of blaming Chancellor Philip Hammond personally, Mr Redwood told BBC Radio 4's Today programme there had been "clear briefing out of the Treasury" that was "not in line with Government policy".
Defence minister Tobias Ellwood acknowledged there was discord in the Conservative Party over Brexit.
In a message on Twitter, Mr Ellwood, who served under Mr Johnson at the Foreign Office until June, said: "Party discord: Think many would agree we are not witnessing our finest hour, at a testing time when poise, purpose and unity are called for."
A Downing Street spokeswoman said the question of Britain paying for access to the European markets was a matter for negotiations and insisted Mrs May had full confidence in the Foreign Secretary.
Asked if the PM supported Ms Rudd's comments that Mr Johnson was "backseat driving", the spokeswoman said: "The Prime Minister values the contribution of all of her Cabinet colleagues.
"They all have huge amounts to contribute."
European Commission spokesman Margaritis Schinas said Brussels would not comment on "an ongoing intra-UK debate" but would wait for Mrs May's speech in Florence.
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