LABOUR has demanded Theresa May kill off a no-deal Brexit as the price of talks with Jeremy Corbyn about finding a way out of the crisis that has paralysed Westminster politics.

After seeing off a no-confidence vote called by the opposition leader, the Prime Minister announced she would invite party leaders in the Commons and other MPs in for discussions to get a Parliamentary consensus.

But she appears to face an uphill struggle after all the opposition party leaders demanded scrapping the possibility of no-deal as a condition of progress, while Labour refused to even sit down with the PM until the concession was guaranteed.

Mrs May did hold talks with Lib-Dem leader Sir Vince Cable, SMP Westminster leader Ian Blackford and Plaid Cymru's Liz Saville-Roberts late on Wednesday.

But Downing Street refused to make such a concession, with the Prime Minister's official spokesman saying: "Want to leave with a deal but she is determined to deliver on the verdict of the British public and that is to leave the EU on March 29 this year."

Asked by a reporter if he was "taking no-deal off the table" in response to the opposition leader's demand, the spokesman replied: "I am not."

Mrs May made a short live television address to the nation late on Wednesday in which she said the talks had been constructive, adding: "I am disappointed that the leader of the Labour Party has not so far chosen to take part, but our door remains open."

Mrs May also aimed remarks at Parliamentarians who voted against her Brexit plan on Tuesday, saying that "MPs have made clear what they don't want, we must all work constructively together to set out what Parliament does want".

She added: "It will not be an easy task, but MPs know they have a duty to act in the national interest, reach a consensus and get this done."

Mrs May will hold further talks with other groups, including eurosceptics in her own party and the Democratic Unionist Party on Thursday.

They will take place the day after she survived an attempt to oust her as Prime Minister, as MPs rejected Mr Corbyn's motion of no confidence in the Government by a margin of 325 to 306.

The Prime Minister's 19-vote victory came less than 24 hours after the crushing defeat of her EU Withdrawal Agreement in the House of Commons, and clears the way for her to start cross-party talks on a Brexit Plan B.

Conservative rebels and members of the DUP who consigned the PM to the worst defeat in parliamentary history on Wednesday rallied behind her to see off the threat of a general election.

Welcoming the result, Mrs May invited leaders of opposition parties to meetings.

She pledged to approach the talks "in a constructive spirit" and urged other parties to do the same, adding: "I stand ready to work with any member of this House to deliver on Brexit and ensure that this House retains the confidence of the British people."

But Mr Corbyn responded: "Before there can be any positive discussions about the way forward, the Government must remove clearly once and for all the prospect of the catastrophe of a no-deal Brexit from the EU and all the chaos that would come as a result of that."

Shadow chancellor John McDonnell later told ITV's Peston that he believed there was currently a parliamentary majority for a "permanent customs union" with the EU.

Mrs May is now due to set out her alternative plan for EU withdrawal to MPs on January 21.

But she risks losing control of the Brexit process, as she must table a motion which can be amended by MPs.

They are expected to use the opportunity to secure Commons support for a range of possible outcomes, from ruling out a no-deal departure or opting for Norway-style membership of the single market to a second referendum.

MPs on both the Remain and the Leave wings of the party warned she needed to make major changes to the deal if she is to get it through the Commons.

Chancellor Philip Hammond reportedly told business leaders after the loss of the meaningful vote that backbenchers would table amendments that would remove the "threat" of a no-deal Brexit.

According to the Telegraph Mr Hammond told executives in Tuesday's call: "My judgement is that there is a significant majority in the House of Commons against no deal.

"What this group of backbenchers has been doing is seeking to find a mechanism by which the House of Commons can express that view in a way which is binding and effective."

Mrs May also held talks with DUP leader Arlene Foster, who afterwards said: "Lessons will need to be learned from the vote in Parliament.

"The issue of the backstop needs to be dealt and we will continue to work to that end."

The EU's chief negotiator Michel Barnier firmly rejected calls from some Conservative MPs and the DUP to drop the Northern Ireland "backstop", intended to ensure there is no hard border with the Republic.

Speaking in Strasbourg he said there would be a "favourable response" from the EU side if Mrs May was prepared to re-think her negotiating "red lines", but added: "The backstop which we agreed to with the UK must remain a backstop. It must remain a credible backstop."