As it says on the tin, have Lord Mandelson become the British Prime Minister with a PoD after his October 2008 return to Cabinet.
Bonus points if you can make him either win a majority in 2010 or form a coalition with the Liberal Democrats.
He returned to cabinet as a Member of the House of Lords; considering that PMs do not come from the Lords these days, it's surely a hard stretch for him to become PM? It would have to be some kind of constitutional crisis for him to take over.
I agree - it would have to be something that took out most of the cabinet, including Brown and Prescott. Mandelson could then act as temporary PM while the Labour Party sorted out the mess (although realistically Blair would probably be drafted in).