THERESA May’s compromise Brexit plan has been labelled “dead on arrival” after the Prime Minister was accused of caving in to rebel Brexiteers’ demands to stave off a humiliating Commons defeat.

Last night, the Eurosceptic Conservative MPs' new clause 36, to prevent the UK collecting tariffs on behalf of the EU unless it agreed to collect them for the UK, which the Government decided to back, much to the annoyance of Remainer Tories, was approved by the skin of it teeth: 305 votes to 302, a majority three.

Such was the anger of some pro-EU Conservatives at Mrs May’s “cave-in” to the Brexiteers that one, Guto Bebb, the Defence Minister, resigned so that he could oppose the Government. He becomes the 10th person to resign over Brexit.

In other votes, Labour's new clause 11, which aimed to establish securing a customs union with the EU as a negotiating objective, was defeated by 316 votes to 289, a majority of 27, and the SNP's new clause 16, requiring the Scottish Parliament's consent to implement several powers in the Bill, was defeated by 316 votes to 36, a majority of 280.

Eurosceptic Conservatives had earlier proposed four changes to the UK Government's Customs Bill aimed at imposing strict conditions on Mrs May after she produced a plan at Chequers that would keep the UK closely tied to Brussels' rules on goods and food.

Just hours before MPs were due to vote on the amendments to the Taxation[Cross Border Trade] Bill, proposed by the European Research Group[ERG] led by ardent Brexiteer Jacob Rees-Mogg, No 10 announced it would not be opposing them, claiming they were “consistent” with the PM’s Brexit blueprint.

Three of the changes - to maintain the Union and not allow a customs border down the Irish Sea, to take the UK out of the EU’s VAT regime and to guarantee there would be no new customs union with the EU without primary legislation at Westminster – seemed to roughly align with the Chequers compromise.

But the fourth - a refusal to collect tariffs on behalf of another country without reciprocity across the continent so that the EU would collect duties on behalf of the UK – did not; not least because the EU27 would not agree to giving Britain preferential treatment.

However, No 10 pointed out a section of the White Paper to justify its argument of consistency.

It reads: “The UK proposes a tariff revenue formula, taking account of goods destined for the UK entering via the EU and goods destined for the EU entering via the UK.”

This, a Downing Street spokesman, made clear the idea of reciprocity was hard-wired into the Chequers Plan.

Yet the paragraph goes on to say: “However, the UK is not proposing that the EU applies the UK’s tariffs and trade policy at its border for goods intended for the UK.”

During Commons exchanges, Mrs May - in response to Labour MP Stephen Kinnock’s claim that she had “capitulated” to the Tory hard Right - was adamant the Brexiteer amendments did not change her Brexit blueprint.

"He is absolutely wrong…I would not have gone through all the work that I did to ensure we reached that agreement only to see it changed in some way through these Bills. They do not change that Chequers agreement,” she declared.

But not everyone was convinced. Her Tory colleague Anna Soubry, a leading Remainer, told MPs it seemed Mr Rees-Mogg was now “running Britain”.

In contrast, Priti Patel, the former International Development Secretary and a prominent Leaver, who tabled the amendment calling for reciprocal action on collecting tariffs, said the PM’s move was "constructive".

Her Brexiteer colleague Peter Bone denounced the Chequers Plan as an “absolute shambles” and called on his party leader to take it off the table.

Kirsty Blackman for the SNP accused the PM of being “held hostage” by the Tory Brexiteers and suggested the Conservative Government was riding roughshod over Holyrood’s voice on EU withdrawal.

The Aberdeen MP said while businesses were desperate for clarity over endless Tory confusion, “we get only in-fighting and a prime minister, who caves in to her extreme hard Brexit wing”.

Outside the chamber, one Brexiteer source boasted how Mrs May's move on the Customs Bill had confirmed "Chequers is dead on arrival".

Earlier, the PM faced a call from leading Remainer Justine Greening, the former Education Secretary, to facilitate a second EU referendum given the parliamentary “deadlock” but No 10 made clear the Government would not agree to such a move “under any circumstances”.

The powerplay over the Customs Bill is just one of several potential flashpoints this week.

After the votes on the Customs Bill, MPs will on Tuesday debate the Trade Bill and the issue of whether Britain should remain in the European single market.

On Wednesday, following the last PMQs of the parliamentary session, MPs will debate Britain's future relationship with the EU and Mrs May will later appear before the Commons Liaison Committee made up of Committee Chairmen.

It is thought David Davis, the former Brexit Secretary, and Boris Johnson, the former Foreign Secretary, will sometime this week make personal resignation statements in the Commons, which will pile more pressure on the PM.

The danger to Mrs May has been underlined by the disclosure that Brexiteers have set up a WhatsApp group to co-ordinate voting tactics, organised by Steve Baker, who last week quit his job as Brexit Minister over the Chequers plan.

It has been suggested more than 100 MPs have joined the group, a number which is more than double the 48 needed to submit letters of no confidence in Mrs May to trigger a leadership contest.

Meanwhile earlier in the day, Scott Mann, the Cornwall MP, became the ninth person to quit their post in protest at the Chequers Plan. The ex-ministerial aide to the Treasury and a former postman, said he would not "deliver a watered-down Brexit".