For British territories, it would probably be something along the line of the Indian experience, but slowed down and drawn out. It might start around the mid-sixties with greater indigenous representation in colonial political offices. Slowly, the peoples of a colony will gain greater representation (overcoming whatever racist systematic blocks the electoral system of each colony puts in their way) until the prime/first/leading minister of the colony is indigenous. Then, a push for independence would happen and the metropole would hold on for as long as possible, making various promises until reality is unavoidable. Maybe sometime around the mid eighties the colony would be ‘granted’ independence in some form of Commonwealth analogy designed to retain benefits for the metropole.
That's if there isn’t an armed struggle for independence, obviously.