Boris Johnson. Though, from articles I've read, he and his inner circle remember well what happened to Michael Heseltine when he challenged Thatcher.
On edit: Polling shows him to be a minus of about 12% were he to be PM. ie 12% less people would support the Tories
Michael Gove. He has been sucking up to the DUP quite quickly. Though it's hard to see him getting the nod; he's a detestable individual.
Home Secretary Amber Rudd might have made a strong challenge. But, I think she won her seat with less than 400 votes after 4 recounts. She pursued that companies should be forced to disclose how many foreign workers they employ. It died when business leaders pushed back
David Davis, the Sec of State for exiting the EU, is rumoured to be interested. He's kind of a mixed bag. On the plus, he's anti-torture and this alone would likely scuttle any chance of taking the PM spot.
He has criticized the government for 'outsourcing torture.' In 2009, Rangzieb Ahmad was whisked to Pakistan where the Inter-Services Intelligence was given the go ahead by the British intelligence agencies to torture Ahmed.
Davis later accused the UK government of trying to gag Ahmed, stopping him coming forward with his accusations, after he had been imprisoned back in the UK.
He went further in Parliament saying, "...an alleged request to drop his allegations of torture: if he did that, they could get his sentence cut and possibly give him some money. If this request to drop the torture case is true, it is frankly monstrous. It would at the very least be a criminal misuse of the powers and funds under the Government's Contest strategy, and at worst a conspiracy to pervert the course of justice."
He is among the signatories of a letter to The Guardian condemning the Coalition's efforts to hide the UK's involvement in rendition and torture behind secret trials
Philip Hammond, the Chancellor of the Exchequer, has had his name bandied about. Mostly because of name recognition than anything else. He's an austerity acolyte. He also has put out some ideas that contradicted party positions (increasing national insurance pension contributions by self-employed persons). The Tories don't hate him. But the parliamentarians are also not thrilled with him being PM
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