But could this sorry bunch do any better?
4/1 Boris Johnson
FOR: The Brexiteer Foreign Secretary is hugely popular with Tory activists and delivered a majority for Leave. AGAINST: He is divisive, does not enjoy the support of MPs and being out of the country hampers bids to build a parliamentary power base.
6/1
David Davis FOR: Brexit Secretary hard man who was in the SAS, he has plenty of experience and gets on well with most Tory MPs. AGAINST: Not entirely trusted by Cabinet colleagues, has overseen stalled Brexit talks and stands accused of pushing for top job.
7/1
Jacob Rees-Mogg
FOR: Comfortable in his own skin, his self-deprecating sense of humour has won an army of Conservative fans. AGAINST: He’s an anti-abortion, anti-gay marriage, Eton-educated, City fat cat multimillionaire who has never changed or nappy or washed the dishes.
10/1
Philip Hammond FOR: Safe pair of hands as Chancellor and has broad experience of Government jobs, including Foreign and Defence. AGAINST: Remainer who is seen as pushing for soft Brexit, alienating pro-Leave members.
10/1
Amber Rudd
FOR: Amiable, confident and forthright, she has performed well as Home Secretary during this year’s wave of terror attacks. AGAINST: She has a tiny majority in Hastings and Rye and nearly lost her seat at June’s general election.
16/1
Andrea Leadsom FOR: Commons Leader is popular with grassroots and made it to final two in last year’s contest. AGAINST: Economically very right-wing and still hampered by comments which seemed to criticise Theresa May for not having kids.
50/1
Tom Tugendhat
FOR: Young, ex-Army officer who commands respect and has just been elected chairman of the powerful Commons Foreign Affairs Committee. AGAINST: Has no ministerial experience and only became an MP in 2015. Can be seen as overly-confident by some colleagues.
80/1
David Gauke FOR: Quiet operator, the Work and Pensions Secretary is well-liked among MPs and could be a John Major figure. AGAINST: He could be too much of a dark horse and the public has no idea who he is.