Former London mayor is favourite to become PM, but home secretary could gain support as unifying candidate

Theresa May, the home secretary, is emerging as the leading choice for a “Stop Boris” candidate among Conservative MPs who want a new prime minister to unify the party after Britain’s vote to leave the EU.

Boris Johnson, the former London mayor, is the clear favourite to succeed David Cameron, who resigned after the referendum result on Friday. Johnson’s decision to campaign for Brexit boosted his popularity with the party grassroots.

Some Tory backbenchers regard Johnson and Michael Gove, the justice secretary, as a dream ticket of popular appeal and strategic brains, particularly given surveys showing they are supported by rank-and-file members.

He is not, however, the clear choice of Conservative MPs, even among the 129 who supported Brexit. One senior Tory who backed leaving the EU told the Guardian they were not convinced Johnson had the gravitas and experience, and would considering backing May if she declares an interest.

May kept a low profile during the campaign, and may pitch herself as a unifying bridge between the Eurosceptic and modernising wings of the party. She burnished her credentials among Eurosceptics during the campaign by calling for withdrawal from the European convention on human rights.

Alan Duncan, a Conservative MP and former minister, said it was wrong to assume the new leader had to be a Brexiter.

“If you just look through the lens of this referendum that is behind us, that will actually narrow the way in which we look at ourselves,” he told BBC Radio 4’s Today programme.

“What we need is unity, stability, credibility and competence. Someone has got to be good on domestic and foreign policy and be able to stand on the domestic stage with dignity and effectiveness.”

Duncan said he would probably not back Johnson and that people should not take it for granted that the grassroots members would either.

“Do not necessarily assume that he is the darling of the Conservative party activists,” he said. “A lot of them have loved the notoriety and the excitement. But actually, once you scratch the surface a little bit and ask the second question, a lot of them don’t want a permanent ride on the big dipper.”

He said MPs “must assert themselves and not be given a stitched-up option ... as a slam dunk”.

“This is the sixth – possibly seventh, actually – leadership campaign in which I’ve been involved and often the poor damned infantry are just taken for granted.

“I think what has to happen here is that every single Conservative MP must appreciate that their view matters and that they have got to look at the long-term future of the country in all parts of the United Kingdom on a whole range of issues.”

Conservative candidates will be invited to throw their hats into the ring as early as this week after the 1922 committee of backbenchers meets on Monday to draw up the rules.

MPs will vote on those names to create a shortlist of two candidates by the end of July. That will be followed by around two months of campaigning and hustings over the summer, before it is put to a vote of about 150,000 Conservative members in September. The result will be announced at the Tory party conference in early October.

Remain supporters suggested on social media that they may join up as Conservative members to stop Johnson and Gove taking over in the same way that Labour membership surged so that people could vote for Jeremy Corbyn.

While Cameron has resigned, George Osborne, the chancellor, has been quiet over the last 24 hours. He is said to have congratulated the leave campaign after their victory, leaving open the possibility that he could stay on in a senior government role after the new leader is appointed.

It is thought unlikely he will run for the leadership having battled so forcefully alongside Cameron to remain in the EU.

Other possible candidates include Amber Rudd, the energy secretary, who clashed with Johnson during one of the television debates and is being urged to run by Tory modernisers, while Andrea Leadsom, Dominic Raab, Liam Fox and Priti Patel are all possible alternatives to Johnson from the leave camp.

Nicky Morgan, the education secretary, a moderniser, is also considering her options, and Stephen Crabb, the little-known work and pensions secretary, is another potential contender.

Gove, who led the Brexit campaign with Johnson, was a favourite among Conservative members polled on the ConservativeHome website, but has repeatedly said he is not suited to the job.

One of his fans, Michael Fabricant, a leave supporter, said: “If Michael Gove does not want to be PM, and I think he would be good, he should be foreign secretary or chancellor and lead EU negotiations.”

The mood among many Conservatives was a desire for unity and an end to infighting, with a view to possibly fighting another election after the appointment of a new leader.

Nadhim Zahawi, a leave campaigner, and Nicholas Soames, a fervent remain supporter, wrote jointly on ConservativeHome before the result was announced that it was time to end the fog of emotion and get on with implementing the Tory programme for government.

Greg Hands, the chief secretary to the Treasury, tweeted that he had the “Brexit blues” but everyone had to move on.

Some of Cameron’s plans, however, such as his life chances strategy due to be unveiled before summer, have been shelved and Whitehall attention is likely to be focused firmly on dealing with the fallout of Brexit.