OK, this is my question.
Can you see that after 1945 is formed British Commonwealth, consisting of: UK, Canada, Australia, NZ and South Africa?
Organisation like today's EU and NATO.
So, common defence pact, free trade, common customs, common currency ( Commonwealth pound ) with common central bank of Commonwealth, cooperation of intelligence and security services, standardisation of military weapons and equipment, common Development Bank. Later Commonwealth Space Agency. Maybe even stronger than EU in foreign policy, with common embassies and consulates, under control of Commonwealth secretary of foreign affaires.
OFC, not all things that today EU does. Not agriculture and deciding of size of cucumbers and such nonsences. Common military projects, joint military command like in NATO...
Other ex-colonies can become associate members of that Commonwealth, but not full-fledged members. So they can participate in some parts, but they have no voting rights. Maybe some smaller ex-colonies can even become members, but not India and such heavyweights.
What is nescesarry to achieve that?