The chances of the Eurocrats appointing anyone with British blood to that position are equivalent to the chances the Cardinals appointing an American Pope. Ain’t gonna happen.
The EU has had Presidents of the European council
Maggie Thatcher (1981 and then 1986), John Major (1992), Tony Blair (1998 and 2005)
And the UK has been President of the Council of the EU a few times: 1981, 1986, 1992, 1998 etc
stranger elections have happened — who would have thought that Karol Wojtyla would become Pope in 1979? A Polish Pope? unthinkable. But it happened.