It is a high-risk strategy but one that could yet result in her becoming the next prime minister. As the Brexit impasse has continued, a resurgent Amber Rudd has emerged as the cabinet minister who has seized the initiative, running a soft Brexit operation that this week forced the beleaguered prime minister to effectively abandon no-deal.

The work and pensions secretary, who only returned to cabinet in November, has helped coordinate a formidable revolt of Tory remainers and soft Brexiters over the last fortnight, forcing a reluctant Theresa May to allow a vote on extending article 50 if no deal is agreed by 12 March.

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Rudd brings to the soft Brexit faction in cabinet and government a degree of organisation that it has hitherto lacked. After she was forced to quit as home secretary last April because of her inability to deal with the Windrush scandal, the titular leader of the soft Brexit faction fell to Phillip Hammond.

The chancellor seemed unwilling to lead an effective caucus in government, complaining on one occasion that after Rudd’s departure there was nobody to organise soft Brexit ministers before key meetings. “You’d think the chancellor would have some convening power, but he didn’t seem to get it,” an ally said.

The standing of the 55-year-old returnee has been boosted by the lengthy Brexit stalemate, because May appears to be no closer to reaching a deal with the European Union with just weeks before the 29 March deadline that she is insistent upon.

Two weeks ago it emerged via leaks that Rudd and three other cabinet ministers had asked May to stop using the threat of no deal as a negotiating tactic in a private meeting; a few days later it was reported that two dozen ministers would be ready to defy the prime minister and vote to delay Brexit.

The extraordinary, open defiance has not pleased Downing Street, which is desperate to close down the endless stream of Brexit leaks from cabinet and other private meetings. Cabinet minutes have been marked secret for some months, when they were not before, meaning they are covered by the Official Secrets Act.

But the defiance of Rudd’s faction has been overt. At the end of last week Rudd co-authored an article with Greg Clark, the business secretary, and David Gauke, the justice secretary, to publicly defy May and argue “it would be better to seek to extend article 50 and delay our date of departure rather than crash out of the European Union on 29 March.”

A frustrated May conceded she could not slap down the “no to no deal” rebels because they had, as Downing Street insiders conceded, the numbers to defeat her in the Commons. Liz Truss, the chief secretary, branded them “kamikaze” ministers in Tuesday’s cabinet, but they still won the argument.

May unhappily read out her proposed compromise to cabinet, one to keep the rebel ministers on board. They were offered a vote on extending article 50 on 14 March if parliament could not reach a deal with the EU by 12 March, and did not vote for a no deal the day after.

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Given there is no majority in parliament for a no deal it was the first victory for soft Brexiters after months where May had tacked right to keep the hard Brexit European Research Group of MPs on board. But in the aftermath, soft Brexiters pushed for more.

A few hours after the compromise was announced it emerged that Rudd and Hammond had told cabinet they wanted May to use any delay in Brexit to face down the eurosceptic wing of their party and forge a new political consensus.

Such successes have brought political problems, however. Hard Brexit Tories say that Rudd and her allies have lacked subtlety. “Yes, they are winning,” said one ERG source, “but they are winning so overtly that there is already a backlash.” Five cabinet ministers briefed the Sunday Times last week in an organic revolt against Rudd, with one accusing her of “astonishing disloyalty”.

But with May living on borrowed time in Downing Street, Rudd supporters – and some critics – argue that the work and pensions secretary could easily make it onto the shortlist of two that is put before party members whenever the leadership contest takes place between now and a general election due in 2022.

One of the arguments deployed is that, unlike fancied runners such as the foreign secretary, Jeremy Hunt, and the home secretary, Sajid Javid, who also supported remain in 2016, Rudd has remained closest to a soft Brexit standpoint; while the two men have moved further away from their natural constituency on the left of the party.

Allies of Rudd’s argue that she remains popular with the grassroots, normally considered strongly pro-Brexit, saying that she raises more money for Conservative associations when she speaks than any cabinet minister barring the prime minister herself, although the claim is impossible to verify.

The ambitious minister’s biggest obstacle could be her narrow 346 majority over Labour in her Hastings and Rye seat on the south coast. Party leaders tend to outperform their parties in elections however, and there always remains the alternative that a friendly nearby MP in a safe seat would make way for her.

But her biggest advantage against a Boris Johnson or another anti-European Union, hard Brexiter could be her unapologetic centrist appeal to the British electorate, a point she reinforced this week when she spoke at a Women in Journalism event in parliament.

Rudd called on reporters present to use language with care when reporting about politics, after telling a story when Leave Mean Leave protesters had gathered around her car, shouting “scum, saboteur”. Incendiary language, she said, was “dangerous; it is damaging, it has consequences, and we have to stop it”.