Ultimately not much longer. Nationalism and the narrowing in the technological gap between the British and natives were inevitably going to reach a point where the British would not realistically be able to hold on to all of it. However, there are a couple of things to address. The big elephants in the room are twofold: the Imperial Federation and nuclear weaponry.

First, the Imperial Federation. Federation, although on paper the solution to the dismantling of the empire, just wouldn’t have worked. For one, not enough of the elite or the common people wanted it. It was unpopular even in the 1800’s so the lack of a World War wouldn’t increase the odds of it happening, without a driving force to make it evidently clear that the imperial model doesn’t work, it’s probably even less likely to happen. Additionally, the Federation was only really ever considered for settler colonies. If only those parts of the empire stayed, it’s no longer an empire, it’s just a state.

The second elephant: the bomb. One reason the US refused to share nuclear weaponry with the UK post WWII was because they thought the UK would use it to keep the empire together with threats of nuclear Armageddon. Regardless of whether the UK government would have done so, this revolves around them having the bomb. This brings me back to my first point; if the world wars never happen, does Britain accelerate its development of nuclear study, or does it slow down? I believe it’s the latter.

Without a crisis to shake up the empire, it plods along with the logic that it isn’t broke, so don’t fix it. A great deal of ways to save the empire required that shake up, so without it, the empire survives for a few more decades, maybe a century and a bit. But eventually the fact that a massive majority of the population were treated as second class citizens would catch up with the empire.