Boris Johnson has said he would be willing to take ‘personal responsibility’ for jobs lost if Britain pursued his Brexit plan instead of Theresa May’s.

Mr Johnson did not categorically rule out standing against the prime minister in a potential contest – something he is expected to do – but said people do not want to hear about “leadership elections and personalities” right now.

The ex-cabinet minister said Ms May’s deal as it stands is an “absurdity” and that she would have to return to Brussels and renegotiate the controversial section on the Irish backstop.

It comes as Tory Brexiteer Esther McVey said she would run for the leadership if asked by colleagues, while ex-cabinet minister Dominic Raab also said he would not rule it out.

Pressure on Ms May and her administration will approach its peak this week, with leadership rivals jostling for position and some MPs suggesting she should resign if she heavily loses the vote on her Brexit deal on Tuesday.

But speaking to BBC 1’s Andrew Marr show, Mr Johnson was asked if he would take personal responsibility for lost jobs if his preferred course of action were perused.

He said: “Yes, of course I will. Do not underestimate the deep sense of personal responsibility I feel for Brexit, for everything that has happened. Do not underestimate how much I care about this.

“This is fundamental to our country and it absolutely breaks my heart to think that after all that we fought for, all that we campaigned for…everybody campaigned for, everybody believes in, that we should consign ourselves to a future in which the EU effectively rules us in many, many respects and yet we have no say around the table in Brussels. That is an absurdity.”

Ex-cabinet minister Esther McVey says she would run for Conservative leader if asked

Sporting a tidier haircut than his trademark ruffled look, Mr Johnson said that at this point people wanted to hear about “a plan to get out of this mess,” rather than a leadership contest.

He also said reports that he already had offered ministerial jobs to MP colleagues in return for support for a leadership bid were “nonsense”.

But asked if he would rule out standing against Ms May for the leadership, he responded: “I will give you an absolute categorical promise that I will continue to advocate what I think is the most sensible plan.

“I’m going to offer you the most sensible plan to get out of this mess. A plan which by the way I think the British people want to hear about.”

Mr Johnson argued that the decision on what to do about the Irish border should be solved at the same time as talks on a future free trade deal, and that a substantial chunk of the £39bn the UK is set to pay to the EU should also be withheld until then.

Brexit casualties Show all 10 1 /10 Brexit casualties Brexit casualties Andrea Jenkyns - Resigned from Parliamentary Private Secretary at the ministry for housing, communities and local government role May 2018 - The Morley and Outwood MP said: “We want to see a new relationship with Europe, with a new model not enjoyed by other countries – nothing that leaves us half-in, half-out. “And in order to achieve this, we need to leave the customs union.” Ms Jenkyn’s also said she wished to dedicate more of her time to Parliament’s influential Exiting the European Union select committee, after a series of “unbalanced” reports produced by MPs PA Brexit casualties David Davis - Resigned from Secretary of State for Exiting the European Union role July 2018 - quit following a major row with May over her plans for post-Brexit relations with the EU. Davis resignation letter said: “As you know there have been a significant number of occasions in the last year or so on which I have disagreed with the Number 10 policy line, ranging from accepting the [European] Commission’s sequencing of negotiations, through to the language on Northern Ireland in the December Joint Report. “At each stage I have accepted collective responsibility because it is part of my task to find workable compromises, and because I considered it was still possible to deliver on the mandate of the referendum, and on our manifesto commitment to leave the Customs Union and the Single Market. “I am afraid that I think the current trend of policy and tactics is making that look less and less likely.” He went on to argue that the “general direction” of Ms May’s policies would leave the UK “in at best a weak negotiating position, and possibly an inescapable one”. AFP/Getty Brexit casualties Steve Baker - Resigned from Minister at the Department for Exiting the European Union role July 2018 - Mr Baker, a key Tory figure in the Leave campaign, was David Davis’s main lieutenant at Dexeu, and was hailed as ”courageous and principled” by other Brexiteer Tories as he also left. Reuters Brexit casualties Boris Johnson - Resigned from Foreign Secretary role July 2018 - resigned over May's Chequers plan. In his resignation letter to the prime minister, Mr Johnson said: "On Friday, I acknowledged that my side of the argument were too few to prevail and congratulated you on at least reaching a Cabinet decision on the way forward. "As I said then, the government now has a song to sing. "The trouble is that I have practised the words over the weekend and find that they stick in the throat." Reuters Brexit casualties Conor Burns - Resigned from Parliamentary Private Secretary to Foreign Secretary role July 2018 - A Brexit supporter who worked alongside Boris Johnson stated in his resignation letter: “I've decided it's time to have greater freedom. I want to see the referendum result respected. And there are other areas of policy I want to speak more openly on.” Rex Brexit casualties Chris Green - Resigned from Department for Transport role July 2018 - The Bolton West MP said: "Parliament overwhelmingly decided to give the decision of whether to leave or remain in the European Union to the British people and they made an unambiguous decision that we ought to leave. "I have always understood the idea in 'Brexit means Brexit' is that the final deal should be clear to me and my constituents - that we have, in no uncertain terms, left the European Union. Twitter Ads info and privacy "The direction the negotiations had been taking have suggested that we would not really leave the EU and the conclusion and statements following the Chequers summit confirmed my fears. "I recognise that delivering Brexit is challenging, however I had hoped at tonight's meeting that there would be some certainty that my fears were unfounded but, instead, they have been confirmed. "I have been grateful for the opportunity to serve as Parliamentary Private Secretary and it is with regret that I offer my resignation with immediate effect." PA Brexit casualties Maria Caulfield - Resigned from Conservative Party vice-chair for women role July 2018 - resigned over May's Chequers plan. Lewes MP warned that the direction of travel did “not fully embrace the opportunities that Brexit can provide”. Ms Caulfield said in her letter to the PM: “The policy may assuage vested interests, but the voters will find out and their representatives will be found out. This policy will be bad for our country and bad for the party. “The direct consequences of that will be prime minister Corbyn.” PA Brexit casualties Ben Bradley - Resigned from Conservative Party vice-chair for young people role July 2018 - resigned over May's Chequers plan. The Mansfield MP said: “I admit that I voted to Remain in that ballot. What has swayed me over the last two years to fully back the Brexit vision is the immense opportunities that are available from global trade, and for the ability for Britain to be an outward looking nation in control of our own destiny once again. “I fear that this agreement at Chequers damages those opportunities; that being tied to EU regulations, and the EU tying our hands when seeking to make new trade agreements, will be the worst of all worlds if we do not deliver Brexit in spirit as well as in name, then we are handing Jeremy Corbyn the keys to No10.” PA Brexit casualties Robert Courts - Resigned from Parliamentary Private Secretary role July 2018 - resigned over May's Chequers plan. MP Mr Courts said: “I have taken a very difficult decision to resign my position as [parliamentary private secretary] to express discontent with the Chequers [plans] in votes tomorrow. “I had to think who I wanted to see in the mirror for the rest of my life. I cannot tell the people of Woxon that I support the proposals in their current form.” Getty Brexit casualties Scott Mann - Resigned from Parliamentary Private Secretary role July 2018 - resigned over May's Chequers plan. "I fear elements of the Brexit white paper will inevitably put me in direct conflict with the views expressed by a large section of my constituents. I am not prepared to compromise their wishes to deliver a watered-down Brexit. "The residents of North Cornwall made it very clear that they wish to have control over our fishery, our agricultural policy, our money, our laws and our borders. I will evaluate those principles against the Brexit white paper and ensure that I vote in line with their wishes." Rex

On the risks that his plan could push the UK towards a no-deal Brexit, he said: “I don’t want no deal.

“We’ve got to be very clear about this. I don’t want no deal, I think what [Brexit secretary Steve Barclay] said just now about the challenges is correct. They are probably exaggerated, but there would be challenges.

“It’s only if you prepare to come out on world trade terms, only if the EU believes that we are serious and willing to negotiate with them as sovereign and equal partners, that they will do the great deal that I think we can do.”

There are said to be a large number of Conservative MPs who believe they have a shot at the Tory crown if Ms May quits or is pushed out in the coming days.

Speaking to Sky News’s Sophy Ridge on Sunday, Ms McVey said she is “looking for a person who can unite the party behind a Brexit deal.”

Dominic Raab says he would not rule out running for Conservative leader

She said: “I have seen the array of people who have come forward at the moment and I think if we can all get behind one...for me the most important thing is not the personalities it is the deal.”

Asked if she would rule out running herself, she went on: “If people asked me then of course I should say, of course should give it serious concern and do it – if people asked me. But at the moment I’m looking at who is in the papers, who can we get behind, but it shouldn’t be about the personality it should be about the country.”

Ms McVey said she would support the prime minister if she were to go back to Brussels and try and renegotiate the deal, in particular around the Irish backstop and the £39bn ‘divorce bill’ that the withdrawal agreement accounts for.

Mr Raab was interviewed on the same show, and asked if he would rule out a run, he said: “I’ve always said I wouldn’t rule it out, but I’m just not going to get sucked in to that debate.

“The public and people watching this show would think it would be very self-indulgent to be engaging in that speculation.”