He insisted he was only continuing to back her leadership because of her promise that EU rule over the UK will be fully scrapped by the end of the transition period in December 2020.
“If that is delivered, 21 months in our island story is 21 months we can cope with,” the senior Tory MP said.
“But if the transition is what the end deal looks like that is very far from being alright.”
Jacob Rees-Mogg’s warning to Mrs May was delivered in a keynote speech to mark the beginning of the final year of Britain’s membership of the EU.
The MP, who is chairman of the Brexit-supporting European Research Group of Tories, also used the address to mock diehard EU Remainers as “cave dwellers” who should observe “a period of silence”.
Jacob Rees-Mogg said Theresa May must deliver a “proper” Brexit that cuts ties with Brussels
Speaking at an event in central London hosted by the Leave Means Leave pressure group, he predicted that the Leave campaign would win “by miles” if a second referendum on the Brexit decision was held.
Mr Rees Mogg admitted being disappointed with Mrs May’s transition deal, agreed by the EU last week, because it kept the UK locked in the Common Fisheries Policy, the Commons Agriculture Policy and a host of other Brussels rules and regulations.
He said during a question-and-answer sessions following his speech: “We’re staying in everything – we’re not leaving anything.”
He said Britain would be “vassal state” during the 21 months from March next year to December 2020, forced to accept EU rules without any say in devising them.
He said: “We will have no representation and we will take their laws. That is not to my mind a good deal.
Mr Rees Mogg admitted being disappointed with Theresa May’s transition deal
The Prime Minister is a very honest person, so I have considerable confidence in her to do what she has said
“The only reason I can stand up in front of you and say we should accept it is because the Government is absolutely clear that we will have a proper Brexit at the end of December 2020, that we will out of the customs union, we will be out of the single market.”
He went on to insist that he had “considerable confidence” that the Prime Minister will deliver a full break from the EU.
Mr Rees-Mogg said: “I am expecting the Prime Minister will get a deal we can all live with, that’s my working assumption.
“The Prime Minister is a very honest person, so I have considerable confidence in her to do what she has said.”
Mr Rees-Mogg criticised Remain campaigners for their noisy attacks on Brexit in recent months.
He joked that, had the Remain side won in the 2016 referendum, he would have taken a vow of silence.
“Had the result gone the other way, though I never thought it would, I looked up that there was a Trappist monastery in Leicestershire. It was my intention to see if they would accept a visit from me, not on a permanent basis but at least on an interim basis,” he said.
He recalled a quote from former Labour prime minister Clement Attlee, who once ordered a colleague to observe “a period of silence”.
Mr Rees-Mogg said: “I thought of that line of Attlee’s to one of his ministers – a period of silence on your part would be welcome – might be something that the winners would have been entitled to expect but it wasn’t what occurred.”
He warned Remainers that their demand for a second EU referendum would backfire against them.
He said: “On the second referendum, we would win by miles. We wouldn’t win on Brexit, we would win on a completely different argument – we would win on democracy.”
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Britons would “be pushed into reversing our minds because the bully boys in Brussels don’t want to give us a good deal,” he said.
“I think we would win the referendum not on the issue of Brexit but on the question of whether our whole democracy is worth a candle.”
Mr Rees-Mogg also insisted that the Vote Leave campaign pledge for taxpayers’ money to be diverted from Brussels to the NHS should be honoured.
Referring to a slogan on the side of the Vote Leave campaign bus, Mr Rees-Mogg said: “I think the electorate looked at that bus that said £350million extra a week for the NHS.
“Leave won, and therefore I think it is incumbent on any government to provide more money for the NHS out of the Brexit dividend.
“Fortunately, the Government has got plans for another £10billion for the NHS anyway and that gets you up to £350 million a week.
“For trust in politics is really important to implement the broad thrust of political policies, not to try and get out of them on technical detail.”