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Theresa May needs to win round all of the Conservative critics of her Brexit deal — or make big inroads with Labour MPs — to offset the opposition of Northern Ireland’s Democratic Unionist party, FT research shows.

As the British prime minister prepares to hold a new vote on Britain’s exit agreement on Friday, she is seeking to make the parliamentary maths work, despite the stance of the DUP, which has been vital to Mrs May’s hopes of winning MPs’ approval.

An FT analysis highlights the scale of the challenge she now faces, which requires winning over all 75 of the Conservative MPs who voted against the deal this month to back the agreement — unless the DUP reverses course.

Alternatively, for every rebel in the Tories’ ranks, Mrs May will need to persuade one additional Labour, or ex-Labour independent, MP to defect — or convince two wavering opponents to abstain.

In her battle to overcome the deal’s two previous defeats — by a record 230 vote margin in January and by 149 votes this month — the UK prime minister has had some success in winning support from Conservative MPs.

After she promised on Wednesday that she would resign as prime minister if the deal is approved, at least 18 Tory Eurosceptics came round — most notably Boris Johnson, former foreign secretary and a potential successor to the prime minister.

Graphic showing what May needs to happen to get her deal over the line when MPs vote on Friday

Others have more ambiguous stances, including Jacob Rees-Mogg, the leader of the European Research Group, the most prominent pro-Brexit Conservative faction in Westminster, who has made his support conditional on the DUP’s assent.

But at least five Eurosceptic Conservative opponents of the deal have indicated they remain intractably opposed: Dominic Raab, Andrea Jenkyns, Julian Lewis, Crispin Blunt, and Steve Baker.

Six Conservative Remainers also reject the agreement in favour of a second referendum — Justine Greening, Sam Gyimah, Guto Bebb, Phillip Lee, Dominic Grieve and Jo Johnson.

If all the MPs in these two groups remain opposed to the deal and the DUP is unyielding in its opposition, Mrs May will need the backing of 11 more Labour MPs. This is in addition to the three Labour MPs, and two ex-Labour independents who backed the deal in this month’s vote.

This could be theoretically possible, since there are over 20 potential Labour targets for Mrs May.

In a novel parliamentary procedure on Wednesday, 25 Labour MPs, plus the former Labour independent Ivan Lewis, broke the party whip to vote against a second referendum — a signal that they could be susceptible to appeals by Mrs May to help see Brexit through.

However, some Labour MPs say that the prime minister will only be able to win over a significant number of converts from the party if they know their votes will really make the difference between victory and defeat for the deal.

Recent comments by Mrs May that fiercely criticised MPs have also not gone down well in Labour ranks, and nor has the prospect that it the agreement goes through it could open the way for Mr Johnson — who is loathed by many in the opposition party — to become prime minister.

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