Plan that just has to work

on goods would not block trade deals if MPs backed her policy.

She also vowed stay on as Prime Minister if defeated, saying: “There is a lot more for me still to do, not least delivering Brexit and being the Prime Minister who takes the UK out of the EU.” Senior Tories, including the deputy chairman James Cleverly, said a rejected deal would threaten Brexit, adding: “Let’s not snatch defeat from the jaws of victory”.

With the resignation of science minister Sam Gyimah, Mrs May is faced with around 100 of her 315 MPs joining Labour, the Lib Dems, SNP and DUP in voting down the deal. Downing Street insiders said she would focus on “winning over MPs” in the next week.

Mrs May is due to open the vote debate on Tuesday. Foreign Secretary Jeremy Hunt and Chancellor Philip Hammond will lay out the foreign policy and economic benefits on Wednesday and Thursday. Meanwhile, the Government is moving towards staying in an EU customs union as its “Plan B” op- tion. A senior source said: “An amendment will be put down to keep Britain in a customs union and Labour are likely to support it because it was their policy.

“Obviously, [it] is not ideal and it means we don’t get one of the biggest benefits Brexit, but no deal is the last option we want.”

It means the UK could not strike its own trade deals with the rest of the world and would be bound by EU trade agreements with no say in them – making Liam Fox’s international trade department redundant.

However, it keeps the UK out of the single market, allowing the Government to stop free movement and regain control of most other laws.

It also prevents problems on the Northern Ireland land border with the Irish Republic and nullifies attempts by First Minister Nicola Sturgeon to whip up support for a second referendum in Scotland. A Cabinet minister said “anything could happen”, but a customs union option was the most likely solution.

The minister stressed the Government cannot allow a no-deal situation “because we are simply not ready for it”, adding: “All we have done is prepared for the worst-case scenarios, but we have not done any of the other preparations.

“Whatever the [Brexit] fanatics think, it will be a disaster if we leave with no deal.”

But there was a gloomy assessment from within the Cabinet of the consequences of a rejected deal.

EU leaders have told the Government any option to act as an alternative for the deal will see them demand the full £39billion “divorce bill”, even if it means preparing for no deal over a transition period.

One Cabinet minister told the