The Prime Minister said threatened Commons revolts this week by pro- and anti-EU MPs risked undermining any chances of a deal with Brussels.
In an article for The Mail on Sunday, she called for MPs to take a “practical and pragmatic” approach rather than face a “damaging and disorderly” Brexit.
But ministers who quit the Government over her negotiating stance attacked the Prime Minister in other Sunday papers - with ex-Brexit Secretary David Davis accusing her of making an “astonishingly dishonest claim” that Brexiteers had not come up with an alternative to her plan.
Steve Baker - a junior minister under Davis - claimed the Brexit Department was little more than a “Potemkin structure to [distract from] what the Cabinet Office Europe unit was doing for the Prime Minister.”
Speaking on the BBC’s Andrew Marr Show on Sunday morning, May hit back at the claims, saying: “Let me very clear that no department was cut out of these discussions. Discussions have been taking place for some considerable time…We have been discussing this option.”
Writing in the Mail on Sunday, May acknowledged some MPs had concerns about her plan for a “common rule book” with the EU for goods and customs traded within what she called a new “UK-EU free trade area”.
However, she insisted that she had yet to see a “workable alternative” to the proposals – agreed by the Cabinet at Chequers – that would ensure trade remained as “frictionless” as possible while avoiding the return of a hard border between Northern Ireland and the Republic.
“We need to keep our eyes on the prize. If we don’t, we risk ending up with no Brexit at all,” she said.
“I know there are some who have concerns about the ‘common rule book’ for goods and the customs arrangements which we have proposed will underpin the new UK-EU free trade area. I understand those concerns.
“It cannot be the breaking up of our precious United Kingdom with a border down the Irish Sea. And it cannot be the destruction of integrated supply chains and just-in-time processes on which jobs and livelihoods depend.”
Her warning came as the Trade Bill returns to the Commons on Tuesday with rival amendments tabled by pro- and anti-EU Conservatives.
She said a series of “wrecking” changes backed by members of the pro-Brexit Tory European Research Group would put at risk the Government’s plans for a “no deal scenario”.
“This could lead to a damaging and disorderly Brexit because without this Bill passing we would not be able to retain the benefits of more than 40 existing trade arrangements; and neither will we have the means to protect consumers, industries and workers from being undercut by unfairly traded goods in a post-Brexit Britain,” she said.
She also warned the Government could not accept an amendment by pro-EU Tories which would keep Britain in a customs union with the EU after Brexit.
“This would be the ultimate betrayal of the Brexit vote. It would remove our ability to have an independent trade policy at all, conceding Britain’s role on the global stage as a force for free trade and endangering people’s jobs and livelihoods. This Government will never stand for that,” she said.
In practice, the Brexiteers stand little chance of success as Labour will not support them while it is unclear whether the pro-EU faction, who largely supported the Chequers plan, will press ahead with their amendment.
Baker said the Chequers plan was the work of an “establishment elite” bent on thwarting the EU referendum vote.
“It does appear to me that there has been a year’s worth of cloak and dagger to land us into the Chequers position,” he told The Sunday Telegraph.
“An establishment elite who never accepted the fundamental right of the public to choose democratically their institutions are working towards overturning them.
“We’re back to what civil servants wanted a year ago, the advice they were giving then, of something like the EEA (European Economic Area membership) plus something like the customs union.
“In terms of who ultimately holds the pen on the papers that go to Cabinet for collective decision, it has been the Cabinet Office’s Europe Unit, and they have clearly been operating to a different ultimate goal to the one what we were operating to.”
Davis meanwhile branded claims that there was no alternative to the Chequers plan as “astonishingly dishonest”.
Writing in The Sunday Times, he said the Cabinet had agreed “concessions to the EU that were so fundamental they risked undermining the whole Brexit process”.
He added: “None of this amounts to taking back control … some are saying that those on the other side of the argument have not worked out an alternative. This is an astonishingly dishonest claim.”