While no one has announced their candidacy for the Conservative Party leadership yet, a senior party figure has already ruled out a vote for Boris Johnson. Sir Alan Duncan, who served as a Minister of State in the Department for International Development, said it should not be assumed that he was the "darling of Conservative Party activists".
"A lot of them have loved the notoriety and the excitement," he told BBC Radio 4's Today programme. "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 added that MP's "must assert themselves and not be given a stitched up option".
He would "probably not" be voting for Johnson, he said.
Sir Alan also appeared to rule out the Chancellor George Osborne's chances, saying he was "much weakened" after anger from MPs over a series of warnings about the economic impact of a vote to leave the EU.
"I feel very sorry for him personally," he said. "If I were to stick my neck out I think it's going to be very difficult for him to stand on the back of this."
He added that only choosing a leader from the Brexit camp would be "stupid", adding: "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."
It is thought Home Secretary Theresa May might consider a run, while Education Secretary Nicky Morgan and Work and Pensions Secretary Stephen Crabb might also throw their hats in the ring.
Whoever wins the nomination will face immediate pressure from European nations to begin immediate talks on withdrawal from the EU.
Announcing his resignation, Prime Minister David Cameron said he would leave it to the successor chosen in October to trigger the two-year process of negotiations envisaged by EU treaties.
But European Commission president Jean-Claude Juncker said the proposed delay "doesn't make sense" and he was backed by foreign ministers of the EU's six founding members, meeting in Berlin for emergency talks on Britain's seismic vote.
Germany's foreign minister Frank-Walter Steinmeier said negotiations should begin "as soon as possible" and Britain had a responsibility to work with the EU on exit terms, while his French counterpart Jean-Marc Ayrault agreed there was "a certain urgency... so that we don't have a period of uncertainty, with financial consequences, political consequences".