THERESA May has attempted to head off a damaging backbench Tory rebellion on her flagship Brexit Bill by making the Remain faction a compromise offer on the post-Brexit customs issue.

Details of the olive branch came as the Prime Minister addressed a key meeting of the Conservatives’ backbench 1922 committee, urging potential rebels not to “undermine” her negotiating position with Brussels by backing a series of Lords amendments to the EU Withdrawal Bill.

Brokered by Sir Oliver Letwin, her former policy adviser, the compromise offer involves tabling a new amendment to the legislation, which pledges the Government to reach a "customs arrangement" with Brussels rather than the Lords’ bid for it to enter a new "customs union" with the EU.

Leading Remainer Nicky Morgan, the former UK Education Secretary, who had been prepared to vote against the Government on the customs issue, made clear she would support the new wording, saying it “buys the Government time”; a customs rebellion could still take place next month when the Brexit Trade and Customs Bills will be debated.

Robert Buckland, the Solicitor General, quoted Benjamin Franklin, the 18th century US politician, after signing the American Declaration of Independence, saying: “We hang together or we hang separately.” He added: “It's more than just about party unity, this is about the national interest.”

The latest move makes it increasingly likely that Mrs May will successfully navigate the series of potential knife-edge votes on Tuesday and Wednesday.

The closest result is likely to come Tuesday morning with the debate on the so-called “meaningful vote,” which would enable MPs to order UK ministers to renegotiate with Brussels should the Commons vote down the proposed Brexit deal this November.

Addressing her party colleagues at Westminster, the PM said: “We must think about the message Parliament will send to the European Union this week.

"I am trying to negotiate the best deal for Britain. I am confident I can get a deal that allows us to strike our own trade deals while having a border with the EU which is as frictionless as possible.

"But if the Lords amendments are allowed to stand, that negotiating position will be undermined," declared Mrs May.

Over the last few days she has been in contact with a number of potential rebels, seeking to persuade them not to oppose the Government.

At the weekend, she received some help when Amber Rudd, the former Home Secretary, and a leading Remainer, was joined by Iain Duncan Smith, the onetime party leader and senior Brexiteer, who jointly called on colleagues to “demonstrate discipline and unity of purpose in support of the Prime Minister”.

Some pro-EU Tories were thought to be backing away amid fears Mrs May could be fatally damaged by defeat, opening the way for a hardline Brexiteer to take over at the top of the party.

Meanwhile, Jeremy Corbyn was facing his own rebellion. One Lords amendment calls for Britain to remain in the single market as part of the European Economic Area, the so-called Norway option.

The Labour leadership believes this would be unsuitable for Britain but Scottish MPs Ian Murray and Martin Whitford have already made clear they will support the proposed change.

Mr Murray, who represents Edinburgh South, said: “The power to save thousands of jobs is in Labour’s hands. If we fail to back EEA membership and allow the Tories to destroy our economy, it will be a shameful day for the Labour Party.”