Britain would probably relinquish its control along more or less the same path. Britain's subjects volunteered to fight for the empire on the understanding that it was the last time they do so. If Independence hadn't been granted independence before the '50s, India would probably become a mega-Vietnam for the British. If World War Two was shorter, then India would probably be the biggest issue on Britain's plate. The Government of India Act in '34 was training wheels for an sovereign Indian parliament, so Indian Independence was a matter of time. Its almost ASB to expect the British to try to hang on in India past the mid '50s without a state of violent insurrection against the Raj.
Once India/Former British Raj is gone, there's not much reason to keep the rest of the Empire. With a few exceptions like Malaya, the Raj was pretty much the only profitable colony for the British. Possessions like Singapore, Suez, or the Persian Gulf protectorates really only make sense as peripheral areas to defend India or access to it. Without India as the keystone, holding onto the rest of the empire doesn't make much sense. The dominion-ization of Canada and Australia provide a good model for the independence process of the rest of the Empire. The British preferred larger agglomerations like the
West Indies Federation and
Malaysia that will congeal or fragment to various degrees.
I don't see a future for some kind of united commonwealth federation beyond symbolic cultural ties, most colonized people choose self-determination when given the option. The fate of Hong Kong depends a lot on whether or not the Japanese end up conquering the western colonies in Asia. British prestige never recovered from the fall of Singapore to the Japanese during WW2.
If colonization is more gradual or haphazard, the world would probably see at least one or two more white-minority pariahs like Rhodesia and more a couple anti colonial insurgencies with generous Soviet support.