What would have become of the empire without the strain of 2 world wars in less than half a century?
It was already moving towards a form of dissolution / dominionisation based on the ideal of the 'colony' nations ability to rule itself.
A much neater, longer, and better organized move towards self rule.
This!
In OTL it was rushed / Pushed due to the UN and Britain's weakness from both World wars - this resulted in many unresolved issues that spilled over to outright war in subsequent years.
Take away the Wars and you have a more stable world, a less powerful UN or equivalent and a much stronger and influential UK able to assert its desire for slower change.
The nations would still get their independence - its just it would be a slower / better process.
I'm aware that not all would agree but I come from the point of view - that the 'Empire' responsible for said 'Colony' nation has an obligation to ensure that the Colony could function in the then modern world before being granted Independence and any handover to be gradual and phased over years if not decades.
This may be a naive ideal on my part and ultimately unworkable - but it should still have been the intention in each case.