THERESA May’s Brexit deal will be “dead” if MPs do not back the UK Government’s Withdrawal Agreement Bill next month, Stephen Barclay, the Brexit Secretary, has conceded.

The Cabinet minister also suggested that if the legislation fell, then two options would remain – before the extended delay to October 31 expires – crashing out of the EU with no deal or scrapping Brexit altogether.

His comments came as the Prime Minister was, for the second week running, told to resign to her face - by a Conservative MP.

READ MORE: Nicola Sturgeon: Theresa May has no chance of passing her Brexit deal 

Mrs May is due to meet the executive of the Tories' 1922 backbench committee tomorrow when she will asked to set out a date for her departure.

However, ministers have already told The Herald that if the PM lost the Commons vote at the Second Reading of the bill[WAB] – the first main vote – scheduled for the first week of June, then she would have to resign.

MPs have, in one form or another, already rejected Mrs May’s deal three times. But the legislation is a much more detailed and, potentially, lengthy process, which will have to secure passage not just through the Commons but also the Lords. Passage of the WAB is necessary to ratify a deal and for the UK to leave the EU.

Appearing before the Lords' EU Committee, Mr Barclay said the legislation would be published "as soon as possible" and then told peers: “If the House of Commons does not approve the WAB, then the Barnier deal is dead in that form and the House will have to then address a much more fundamental question between whether it will pursue...a no-deal option or whether it will revoke."

Later, David Jones, the former Welsh Secretary, said: “No 10 now realise once this has been introduced, if it is rejected, that is the end of the Government's strategy; it is really high-stakes politics.”

The Tory Brexiteer told BBC Radio’s World at One: "[The PM] has staked her personal prestige upon the Withdrawal Agreement. She's had three rebuffs now and it's very hard to see where she goes after a further rebuff if the bill, when it's rejected, can't be reintroduced.

READ MORE: Council elections ‘plague on both your houses’, Ruth Davidson tells Tories and Labour 

"If that bill is rejected, then it seems to me the whole policy is dead and can't be pursued any further," he added.

Last week, Tory backbencher Andrea Jenkins called on Mrs May to go; today, it was the turn of her Conservative colleague and fellow Brexiteer Peter Bone.

The Northamptonshire MP told MPs he had been out campaigning with a group of Conservative supporters in his Wellingborough constituency at the weekend, who had given him a message to deliver in the Commons.

He told the PM: "They say that her deal is worse than staying in the EU, that they want us to come out now on a no-deal basis, and third, more importantly, they've lost confidence in the Prime Minister and wish her to resign before the European elections…What message do you have to say to these loyal and dedicated Conservatives?"

Mrs May said she thanked all party supporters for their work campaigning and fundraising, and said to those "concerned about delivering Brexit" her Government "wants to deliver Brexit and has been working to deliver Brexit".

The PM added: "Sadly so far, the House of Commons has not found a majority to do that. If everybody in the House of Commons had voted along with the Government and the majority of Conservative members of parliament we would already have left the European Union."