Video report by ITV News Correspondent Angus Walker
Ruling out a no-deal Brexit as a price for face-to-face talks is an "impossible condition" because it is not within the Government's power to do it, Theresa May has told Jeremy Corbyn.
The Prime Minister responded on Thursday afternoon to a letter from the Labour leader demanding she remove the threat of crashing out without a deal before they can meet.
In her reply to Mr Corbyn, the PM said: "I note that you have said that 'ruling out' no deal is a precondition before we can meet, but that is an impossible condition because it is not within the Government's power to rule out no deal.
"Let me explain why. Under Article 50 of the Treaty on European Union and the Withdrawal Act 2018, we will leave the EU without a deal on 29 March unless Parliament either agrees a deal with the EU or the UK revokes article 50 and chooses to stay in the EU permanently.
"So there are two way to avoid no deal: either vote for a deal, in particular a Withdrawal Agreement, that has been agreed with the EU, or to revoke Article 50 and overturn the referendum result.
"I believe it would be wrong to overturn the referendum result."
Her comments come as Mr Corbyn urged Labour MPs not to engage with the Government until a no-deal Brexit is taken off the table, a condition he has made clear in a letter to Mrs May.
The Labour leader sent a letter to members of the parliamentary party after Hilary Benn, Yvette Cooper and John Mann all visited the Cabinet Office in Whitehall on Thursday.
Speaking in Whitehall Mr Benn said: "We made it very clear that the Government has to rule out no-deal that is the first step they have to take.
"And secondly the prime minister needs to change her red lines."
Their visits came just hours after Mr Corbyn had used a speech in Hastings to reiterate his demand that a no-deal Brexit must be ruled out before he would take up Theresa May's offer of talks.
Meanwhile, ITV News has seen a government document, handed to MPs involved in Brexit talks, which suggests that organising a second referendum would take up to a year to organise.
When asked about Mr Corbyn's letter to MPs Mr Benn said he was not aware of it, adding that he and Mrs Cooper had attended the talks as chairs of cross party committees.
In the letter to MPs, Mr Corbyn wrote: "The Prime Minister has offered to open talks with Opposition Parties, however, I have been absolutely clear that any starting point for talks about breaking the Brexit deadlock must be on the provision that that the threat of a disastrous ‘no deal’ outcome is ruled out.
"This is a position that has now been adopted by the First Minister of Scotland, Nicola Sturgeon.
"I urge colleagues to respect that condition and refrain from engagement with the government until ‘no deal’ is taken off the table."
Mr Corbyn's comments come as he told Prime Minister Theresa May he would only enter talks over her Brexit deal if she takes "no-deal off the table."
After seeing off a vote of no-confidence in her Government on Wednesday, Mrs May had invited the other party leaders for individual talks to find a way forward on Brexit.
The Leader of the Opposition responded to Mrs May's call for cross party talks during a speech in Hastings, a marginal Conservative constituency.During his speech Mr Corbyn branded Mrs May's offer to reach out across party lines as "a stunt."
His comments come as Mrs May said she was "disappointed" Mr Corbyn had "chosen not to take part, but our door remains open".
However the Labour leader said he had already outlined an "alternative framework" regarding a "better" Brexit deal, in his letter to Mrs May.
During his speech in Hastings Mr Corbyn addressed the possibility of an extension of the Article 50 negotiation period, saying: "Quite clearly, if no agreement has been reached within the time it could be implemented by the end of March, the issue of extending the exit date, extending Article 50, does come into play.
"Indications are that that may well be the case."
He also made clear his preferred outcome remains a general election, though he said the option of supporting a second referendum remains "on the table".
He left open the question of which side Labour would campaign on in a public vote: "If a second referendum should take place, then obviously the party will decide what role we will play in that and what our view would be.
"But I can't really go along with the idea it should simply be a re-run of what happened in 2016. There has to be a discussion about the options that we put forward and we've put forward the three options that I've outlined."
Mrs May has held talks with Lib-Dem leader Sir Vince Cable, SNP Westminster leader Ian Blackford and Plaid Cymru's Liz Saville-Roberts late on Wednesday.
The Prime Minister's official spokesman said: "We 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."
MPs are due to vote on the prime minister's Plan B on January 29.
Responding to Mr Corbyn's speech, Mr Cable said: "Since he appears to be determined to play party political games rather than acting on the wishes of his own members and MPs, he will no longer be able to rely on our support for further no-confidence motions.
"I believe other parties are taking the same view. It's time Mr Corbyn got off the fence and made his position plain."
Conservative Party chairman Brandon Lewis said on Thursday Jeremy Corbyn's stance on talking with Theresa May is "hypocritical".
He accused Labour of "playing politics rather than getting real".
Speaking in Downing Street on Wednesday night, the Prime Minister urged politicians to "put self-interest aside" and reach an agreement on a Brexit plan.
May said: "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."
But Labour leader Jeremy Corbyn said he would not be meeting with the Prime Minister until no-deal was taken off the table, accusing her of "blackmail."