That's a good question to think about actually. I don't think they handled it the way Russia is handling it now (assuming that this is in fact what's happening with Russia).
Actually the big European powers gave up their empires fairly quietly. Yes they sometimes fought wars to keep them on a case by case basis, but I don't think any of them launched large scale campaigns of invasion as a response.
I am sorry but Ireland, Kenya, the Malayan emergency, the Indian mutiny, the Vietnam war, Portugal’s wars, Algeria, Suez, Spain from 1820s+…
I would not call any of that quiet. And Suez was definitely an invasion.
Hell, US hegemony was challenged by Al-Qaeda and they invaded Iraq.
Russia is different in that rather than being a seaborne empire they were a land based empire. The Austro-Hungarians invaded Serbia when their Balkan ambitions were looking like being thwarted.
There were also significantly counter-culture movements against anti-imperialism similar to the russian anti-woke-culture war (after all it discredits imperialism) and thus dissolves the russian empire if looked at through this lense. They were just discredited after hitler dialed imperialism up to eleven.
The British empire peacefully transferred power to their descendents/cousins, this is a success story. Speaking english. Christian. Shared ancestry.
Besides, we are not talking about breaking up the empire. That already happened with the dissolution of the USSR. We are talking about the extinction of a nation.
It would be like if the UK was split into Scotland, a puppet of the EU. Wales, a quasi independant state with strong ties to Scotland. England, a former power center. Finally Ireland becomes whole.
Do you really think the brits will be cool with this, especially if lets say Russia/China was working behind the scenes to make it happen and the so called ally EU was all too happy to gain all this new power and influence...
For the UK, France, Spain, Portugal it was overseas empires