OK, here's my shot:
Nasty seizes all of Continental Europe (Nazis/Communists/altDraka). The 'Free World', under US (if WWII era) or UK (if WWI era) leadership (as the strongest remaining power) unites militarily (think something like a bigger and stronger NATO), and invades Europe to defeat the bad guys. The bad guys have the resources of the entire continent to play with, and no (significant) distraction of another front.
Thus the build-up takes a decade or so, and the invasion another 5-10 years. (Kind of like CalBear's Anglo-American Nazi war).
By the end, Britain (and all her Commonwealth daughters) and the US (and many Latin American countries) have fused into a single entity (perhaps formally called an alliance, but functionally a single country). The bad guys (initially) and then the fighting have pretty much destroyed the infrastructure and former states in Europe, and the occupied deBadGuyified areas are gradually adopted into the Union as they re-achieve 'civilization'.
How's that?