- Video report by ITV News Political Correspondent Libby Wiener
Transport minister Jo Johnson has resigned over the Government's Brexit direction, arguing that the deal currently in the offing would be a "terrible mistake".
Mr Johnson, brother of former foreign secretary Boris Johnson, announced his decision in a letter and video on Friday.
The MP for Orpington, who voted Remain in 2016, said that the current situation meant the UK was facing either "years" of economic uncertainty or a no-deal scenario.
In recent days, talk has increased that the UK and Brussels are near to striking a deal.
Speaking shortly after his resignation announcement, Mr Johnson said he would back a second referendum because what was on offer was "radically different" to that promised during 2016 campaigning.
"We are barrelling towards an incoherent Brexit that is going to leave us trapped in a subordinate relationship to the EU with no say over rules that will govern huge swathes of our economy," Mr Johnson said in his resignation video.
"This is completely unacceptable and unsustainable for a proud democracy such as our own.
"So great is the gulf now between what was promised in the referendum campaign and what is on offer in the prime minister's proposed deal that I have had no choice but to submit my resignation."
Mr Johnson added that it was "imperative" that the government go back to the people and "check that they are content to proceed on this extraordinary basis".
He said: "We will be, instead of in Europe but not run by Europe, we will be out of Europe yet wholly subject to European rules."
Mr Johnson continued that the deal being negotiated would effectively leave Britain a vassal to the EU.
"It's not going to deliver trade deals, our ability to strike meaningful trade deals is going to be greatly reduced," he said.
"It's not going to lead to us becoming a Singaporean, turbo-charged economy on the edge of Europe - far from it.
"We're going to be signing up to all the rules and regulations over which we will not longer have a say."
Mr Johnson's siblings Boris, and his television personality sister Rachel, both tweeted their support.
The ex-mayor of London, who himself resigned over Theresa May's Chequers plan, wrote: "Boundless admiration as ever for my brother Jo.
"We may not have agreed about Brexit but we are united in dismay at the intellectually and politically indefensible of the UK position.
"This is not taking back control. It is a surrender of control. It does not remotely correspond to the mandate of the people in June 2016."
A Downing Street spokesman said: "The referendum in 2016 was the biggest democratic exercise in this country's history. We will not under any circumstances have a second referendum.
"The Prime Minister thanks Jo Johnson for his work in Government."
Mr Johnson's resignation came as Chancellor Philip Hammond told ITV News he hoped nobody would resign over the potential deal.
Asked if a deal could be agreed without any casualties, Mr Hammond said: "I very much hope so.
"I hope in the end we're a Cabinet of pragmatists. I think of all of us on all sides of this argument know that we're not going to get everything we might have wanted when we went into the negotiation.
"Practical politics is about making sensible compromises."
Fears have been growing that Mrs May may agree a deal with the bloc which results in different customs arrangements for Northern Ireland.
Many people have highlighted this issue as one of their red lines.
DUP leader Arelene Foster told RTE News that she would not support Mrs May's decision to have a Northern Ireland-specific backstop resulting in a border down the Irish Sea:
"No unionist would be able to support that," she said.
"In other words we (Northern Ireland) will have a different regulatory system from the rest of the United Kingdom, and essentially there's going to be a border down the Irish Sea."