The frontrunner in the Tory leadership contest Boris Johnson has said the UK will leave the EU on October 31 with or without a deal and he has already made it clear he will only appoint ministers who are prepared to back a no-deal Brexit.
Mr Gauke has warned about the economic impact of a no-deal Brexit and when he was asked if he thought he would be sacked by Mr Johnson on the BBC’s Andrew Marr show, he replied: “I suspect that I will possibly have gone before then.
“If his position is that he is going to require every member of the cabinet to sign up to being prepared to leave without a deal on October 31, to be fair to him, I can’t support that policy so I would resign in advance.”
Mr Gauke has been dubbed as a “pragmatic Remainer” who backs a soft Brexit and wants the UK to maximise access to EU markets after leaving the EU.
Last week in a speech to judges in the City of London, Mr Gauke said: “I’m the first Lord Chancellor in a while to have served long enough to deliver two of these speeches.
“How times have changed, I might only have three weeks.”
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This comes as the Tory MP Sam Gyimah said he believes that more than 30 Tory MPs are set to vote against a no-deal Brexit.
He told Sky News: "I wouldn't want to announce them before they have been tested as being viable."
"But there is a real concern. The real concern here is not about Leavers or Remainers. The real concern here, is that this is not in the interest of our country."
This weekend Home Secretary Said Javid gave his support to Mr Johnson saying he was “better placed” than Mr Hunt to “deliver what we need to do at this critical time”.