Jeremy Hunt and Michael Gove among the Tories who could try to succeed Theresa May

At least 10 cabinet ministers are considering putting themselves forward to take over from Theresa May as prime minister after she promised to step down if her Brexit deal passes.

Sources said Jeremy Hunt, Sajid Javid, Amber Rudd, Michael Gove and Matt Hancock are all considering their options, having been urged to run by fellow MPs.

Liz Truss, Gavin Williamson, Andrea Leadsom, Stephen Barclay and Penny Mordaunt are also understood to be weighing up leadership bids.

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With May still struggling to pass her agreement and parliament paralysed over the options, speculation is rife among Conservative MPs about the frontrunners to replace her.

There are also numerous backbenchers preparing to throw their hats in the ring, including Boris Johnson, who is backed by Jacob Rees-Mogg, the darling of the Tory selectorate.

The former Brexit secretary Dominic Raab also has an advanced and organised campaign, with a well-staffed political consultancy helping him, and a Facebook page of “grassroots” activists with the slogan “Ready for Raab”.

He has positioned himself as the most hard-Brexit candidate holding out against May’s deal, but a source close to a rival campaign said this would isolate him in the party “along with 15 or so hardcore Eurosceptics that it doesn’t look good to have backing you”.

One aide working for one of the frontrunners said “around 20 will run but most people will tuck in quite quickly behind the big players”. The deputy Conservative chairman, James Cleverly, and the Plymouth Moor View MP, Johnny Mercer, who were both first elected in 2015, are thought to be considering leadership bids with a view to enhancing their profiles.

Friends of Hunt, who has been assiduously courting Tory MPs and tacking to the right to win over Brexiters, said he was concentrating on his day job but was likely to have a crack at No 10 when a vacancy arises. Meanwhile, those close to Javid, who has won support, said it was too early to say but they were not dismissing the prospect.

Gove, the environment secretary, has also been quietly assembling a leadership team, and is regarded by centrist Tories as a less alarming option than Johnson, the former foreign secretary. “There’s definitely people urging him to run,” said an ally. There is also talk of the possibility that Gove and Javid could be running mates.

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David Davis, the former Brexit secretary who was defeated by David Cameron in the 2005 leadership contest, is also not ruling himself out, although friends said his focus is on the tumultuous next few weeks of the Brexit process.

The work and pensions secretary, Amber Rudd, one of the ringleaders of the “Gaukeward squad”, a group of ministers around the justice secretary, David Gauke, who have been pressing the prime minister to do more to avert a no-deal Brexit, is being courted by several candidates as a potential backer.

She has not definitively ruled out a campaign for the leadership, but is regarded as a strong potential running mate, particularly for a Brexiter keen to shore up their standing with the party’s remainers.

Rudd was spotted having breakfast with Hunt on Wednesday, and a friend said conversations had also taken place with Javid, adding: “She’s extremely in demand with top-tier candidates.”

The friend said Rudd was “very close” to Johnson, of whom she said in a televised debate during the 2016 EU referendum campaign that he was “not the man you want driving you home at the end of the evening”.

Some MPs looking for a carrier of the Cameronite flame are turning to Hancock, the health secretary who was an adviser to George Osborne. An ally of his said: “He’s being urged by loads of MPs to run as the ‘fresh-start’ candidate.” Barclay, who is considered a good media performer, is another name being mentioned by MPs as someone they believe could be an effective new face.

Williamson, the defence secretary, has also not ruled out running, although he is thought to be positioning himself more as a kingmaker, since he has many parliamentary allies from his time as chief whip. He could run but bow out to bring his supporters in behind one of the other candidates.

Truss, the chief secretary to the Treasury, is among those known to be considering a leadership bid and has been giving wide-ranging speeches setting out her brand of free-market Thatcherism. Mordaunt and Leadsom, both Brexit supporters, are also understood to be considering running.

Among the senior figures not expected to run are Brandon Lewis, the party chairman, Chris Grayling, the transport secretary, and Philip Hammond, the chancellor, who acknowledges that he is not popular enough. David Lidington, May’s de-facto deputy, has been touted as a possible caretaker leader, but said this weekend that being close to the office of prime minister has cured him of any ambition, and Gauke dryly said he was “resisting the clamour”.