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Theresa May is under growing pressure to postpone a third Brexit vote after a suggestion that she would replace her chief EU negotiator to get her deal through left her still facing defeat.

A meaningful vote that was widely expected tomorrow night could now be held on Wednesday or moved to next week unless there is a major breakthrough this evening.

In a desperate last ploy to save her deal, Downing Street has told Tory MPs that Mrs May’s chief Brexit negotiator Olly Robbins will quit if it goes through.

One MP was told that Mrs May would “update her negotiating team” before the next phase of talks, while another was told that Mr Robbins, a bête noire of the European Research Group of Tory Brexiteer MPs, would “go as soon as the deal is through”.

Neither of the MPs was persuaded to back the deal, however.

Mrs May is now banking on her Northern Irish DUP allies to back her deal, but a source in the party said there was “plenty still to do”. Moreover, about 30 Tory MPs were still resisting backing Mrs May, enough to sink the deal.

In more key developments:

Cabinet ministers believe Speaker John Bercow will not allow a fourth vote on the deal, and are advising Mrs May to postpone it to next week unless she is certain of winning.

Downing Street rejected a demand by Boris Johnson that Mrs May go back to Brussels to seek concessions, saying there will be “no further negotiations” on it.

The DUP was in talks with No 10 over a reported “Stormont lock”, which would ensure that the whole of the UK, rather than just Northern Ireland, is impacted by the backstop to avoid a border in the Irish Sea. There were also rumours of a new money deal being offered to Northern Ireland.

An attempt by Mrs May to appeal to “patriotic” MPs backfired as Right-wingers said it was an insult to call them unpatriotic.

Jacob Rees-Mogg, chairman of the ERG, hinted he might back Mrs May, but 23 ERG MPs wrote a letter to the Daily Telegraph making clear they will not shift.

A ring-round of MPs over the weekend, led by Cabinet ministers and Mrs May herself, appeared to have picked off only a few of the 75 MPs that Mrs May needs to back her.

The Prime Minister’s spokesman said: “It’s a matter of fact that if there is a vote that is going to take place on Wednesday, then the deadline for tabling that motion would be Tuesday evening.”

No 10’s suggestion that Mr Robbins will leave if the deal passes failed to win MPs over. One told the Evening Standard: “What colleagues want is to see a change at the very top ... That means a new Prime Minister.”

Another MP said: “You can read between the lines a strong hint that he will go. But it doesn’t matter. She would be wise not to hold a vote this week.”

The Standard asked No 10 for a comment.

The core of ERG hardliners, said to number between 20 and 40, appeared to be holding firm against Mrs May’s deal today.

Mr Rees-Mogg said he had not made up his mind and was waiting to see what the DUP decides. “No deal is better than a bad deal, but a bad deal is better than remaining in the Europe Union,” he said on LBC radio.

“We have got as close to leaving as we will ever get under these circumstances. If it is thwarted now, no one is ever going to allow us another chance to have a vote. The whole weight of British establishment opinion will prevent that ever happening again.”

Some Tory MPs are demanding the Prime Minister promises to quit in June as the price of her deal, so that a new leader can negotiate the second phase of Brexit talks which will forge a future trade and security relationship with the EU.

Ex-Cabinet minister Sir John Redwood, one of the signatories of the letter to the Daily Telegraph, dismissed the withdrawal agreement as “a very expensive invitation to more talks” and told BBC Radio 4’s Today programme: “It violates the Conservative manifesto in many important ways. The manifesto is very clear that no deal is better than a bad deal.”

He said that “a lot” of Conservative MPs shared his concerns, but declined to estimate how many would vote against Mrs May’s deal.

Peers today warned of the constitutional implications of any “Stormont Lock” which Mrs May could strike to persuade the DUP to back her deal, stressing that they would want to properly scrutinise any legislation.

Ministers, including Philip Hammond, have been in intensive talks with the DUP to try to get them on board. The Chancellor’s involvement has sparked accusations that the Government will offer a “Brexit bribe” to the DUP, possibly £1 billion of extra cash for Northern Ireland. But the party has denied taking part in a financial “auction” for its support.