Bear with me, before leaping for keyboards to shout "that'll require the magical existence of extraterrestrial winged mammals".
So...for some reason post WWII, Germany can't or doesn't involve itself with a pan-European movement. France is understandably going to look at the Commonwealth with renewed interest, as I believe did Norway anyway.
Could an EEC-like association between the Commonwealth powers arise? ie, working towards a customs union with a combined external tariff, freedom of movement for the goods/capital/services/people. Probably a NATO style alliance of some sort (committing your allies to help you, but not necessarily militarily).
The relationship with the US would be crucial for Canadian entry, maybe some gesture towards US trade? How would the US react?
The UK, Canada, Australia, New Zealand & France would obviously form the core, with Denmark probably following Norway in, and Benelux probably following France. Who else could you see joining? Obviously the distances present a challenge, but here there would probably be regional areas which might serve to encourage co-operation - Canada & any Caribbean entrants (and the US to a certain extent), Europe & any North Africa entrants, Australasia/Austronesia.
Malta & Cyprus immediately spring to mind for me. South Africa would quickly be shunned due to apartheid I'd assume. Singapore maybe after it's separation from Malaysia. Would anyone else be interested (from anywhere)?