Prime Minister of the British Empire… who?

Sometime in the first decade or two of the 20th century the British Empire puts itself together to the point of having an Imperial Parliament (foreign affairs, trade, military, that sort of thing). I'm having trouble figuring out British political figures that would give up on domestic UK things in my timeline.

Who are likely potential Prime Ministers?

Arthur Balfour might make a move as might Bonar Law. Robert Cecil perhaps?

I can't see Asquith or Lloyd George giving up on UK domestic reform to move up there. Sir Edward Grey?
 
Bonar Law, Cecil, or Lloyd George. Definitely not Asquith, because as soon as we get into a prolonged political crisis his spine will evaporate. See Strange Death for details.
 
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