Former foreign minister Boris Johnson, who quit in July in protest at the Chequers plan, launched a fresh attack on it in his weekly newspaper column on Monday.
But last night it was reported that Brussels was preparing to accept a frictionless Irish border using new technology to minimise checks.
Under the European Union plan, goods could be tracked using barcodes on shipping containers under "trusted-trader" schemes administered by registered companies, the Times reported.
May has proposed that Britain follow European Union rules in trade in goods after Brexit, to protect manufacturing supply lines and avoid a "hard border" between Northern Ireland and Ireland. But Mr Gove, one of the leaders of the Leave campaign, urged fellow Tories to support the plan in order to secure Brexit, rather than risk an impasse in Parliament or a general election.
"It's ensuring that we get that good deal from the European Union which is good for people in the United Kingdom, wherever they live in the United Kingdom, that's what's important for us".
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He said it will be up to the House of Commons in the future to "chart this nation's destiny" and decide what to do if Brussels law changes.
The only alternative to the Chequers plan is crashing out of Europe with no deal, Theresa May has told a BBC interviewer.
One event, organised by pro-Brexit group Leave Means Leave, will take place in Birmingham later this month while the Conservative Party conference is being held in the city.
Khan denied claims he had called for the vote in order to distract from his record as London mayor, saying a record number of homes had been started in the capital previous year.
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London Mayor Sadiq Khan has this weekend called for the outcome of the Brexit negotiations to be put to the British people in a referendum. And I think that would be a profound mistake'.
"He told the presenter: "'For the first time the British public should have a say on the outcome of the negotiation.
He dismissed suggestions he was trying to distract from his track record as mayor.
Sadiq Khan's call for a second referendum gains importance because he is a senior leader of the Labour Party-Britain's current opposition party, Reuters said in a report.
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Khan said: "The need for another public vote on Brexit was never inevitable, or something I ever thought I'd have to call for".