I suspect you may need a WWI to force Europeans to realize they need a proto-EU.
I think that WWI is still early enough to save the various empires ( in some form - India is going to go 'independent', but maybe as part of a tighter commonwealth.)
If there is the possibility for 'colonies' to advance to being (junior at least) members of this federation, it would help in the future. So, for instance, the 'white Dominions' might all be 'junior' members (only junior, still the Westminster conference is probably butterflied away, and none of them are truly 'independent' yet). How all that would play out in the future, who knows.
Heck, this could be the nucleus for an effective world government! You've already got all Europe, half of North America, half of Africa (and mounting), all of Oceania, south Asia, most of South East Asia.
If Brazil and the south american countries were allowed in (as ex-colonies, or as 'European' in culture), then we're well on our way to world domination...
If enough of the world joins, even the US might (trade trumps a lot of things).