Is your scenario?
Britain and France quickly killed off the Nazi threat around 1936
The empire restructures as a trading union
The UK benevolently assisting the various constituent parts to become self-governing
That's not really an empire. It's the EU with different countries.
Would the world be better off?
WWII and the Nazi's would have claimed fewer lives.
The former Empire countries would be about where they are now but perhaps have more trading power. What about the other European Empires would they create their own trading blocks within their empires rather than the EU?
Maybe America would have been less dominant during the end of the 20th C. Is that a good thing? Britain and France, I think would need to fulfil that role.
But the Soviets would still be in place in Russia. Would that be better than Putin? Where would the Iron Curtain fall.
Germany, I guess would fall under British and French influence. But is will the post war settlement be fair? Would it return to the same situation it was in the early thirties.
Then there's Japan. I think the world's better off with democratic Japan than it was with the Japanese Empire. Maybe America would still have gone to war with them?
Technological advancement in the 40's would have been slower without the War. Would we have caught up now?
By the time the world reached 2024, I think Britain would be quite similar to what it is now. We'd have still have had inward immigration from the former empire. Would Britain be any happier seeding it's sovereignty to an alliance with Canada, India, Australia than it was EU.