Dr Alf’s criteria “trusted wily heavy hitter” have to be supplemented by the words “telegenic” and financially savvy.
Jeremy Hunt seems too lightweight for that, given his failure to deal with the Junior doctors fast enough and effect NHS reform; Boris Johnson vacillates and is light on detail and divisive; Mrs May is cold, and as a person who has upset the police, the Chinese Government and failed to effect police reform, does not fit the bill either.
I think one needs to drill downwards into next generation territory to find the person needed who should perhaps be a woman because they are better at bridge building, consensus creating than men.
In the end, one might be hard pressed to find someone who has all the required qualities that Dr Alf has identified so I see a compromise candidate who will have to be assisted by expert negotiators “bridgers”, “thrusters” and “schmoozers” as the Australians and those who know some Yiddish would describe them.