Having pondered this from a more significant departure, the non-belligerence of the UK in the Great War, thus not merely no "WWII" but also no significant impact upon the Dominions, settler colonies and other possessions. My thinking is that it all hinges on India, it was the keystone of the Empire and in many ways its reason to exist. It is little wonder why the Empire faded almost overnight once India gained independence. Thus I think you need to discern when India is ready, willing and/or able to break away. And you need to consider if it is a peaceful separation or a violent divorce. Once India is out and depending on its hostility, I think you have a finite clock for the rest.
Another good bell weather would be Canada or South Africa. The former found itself drawn into the orbit of the USA and wealthy enough to abandon Britain. South Africa saw its internal political debate overtaken by the Dutch rather than English influenced populace who went on to effectively renounce their ties to Britain. That may have been as much the unhealed wounds of the Boer War but it shows that even the "white" and "British" colonies were not locked into Empire.
The Empire had plenty of cracks that were open to breaking apart a more adroit London would have transitioned to a stronger trade bloc centered on the Pound and mutual defense alliance centered on the strength of the Royal Navy. There may be reasons why that was a steep climb and one can debate whether or not it could occur. For me I look at the rising education of the indigenous elite who absorbed British cultural and political ideals yet faced its hypocrisy n action at home, they would agitate and ultimately cause the crisis, the elite in London were just as likely to ignore the pain of change until they were already at the precipice. It is often human nature. India was primed by the end of WWII to seek independence, but that in part relied upon the experiences of fighting Britain's wars, India manned the armies and suffered, and in WWII we see the Atlantic Charter following the 14 Points, more and more ideals that undercut the validity of old colonialism. Wash all that away and who knows, but I tend to think that the clock was ticking. One might give another generation to British India and it might have fragmented rather than sought independence mostly united. each step taken defines how it happens, for me I think India was going to be ready for a new arrangement somewhere in the 1940s to 1970s as its economy improves and its wealth ticks upward. My feeling is that London will resist but ultimately succumb to independence. By then I think even Dominion status will not work as India will look like Canada, able to stand on its own, and Canada is quite independent of London. But that is not to say that an intervening several decades or generations of peace might not influence a stronger sense of fraternity.
My minimum confidence is that the UK holds a few more strategic bits, it has a more defined place as a great power, it has better trade links and stronger ties to more of its former colonies. In other words I think Britain looks more like France with regard to its former colonies longer than it did. If if the British fall short of being a distinct pole in the post-war world, it should be more obviously at play past the 1970s. Europe is where it has the most interests but I think Britain in this scenario is a more often than not serious regional actor in several key areas centered on the Arabian Gulf, Singapore and perhaps Western Africa and/or Southern Africa. This Britain is far more partner in Western actions than a sort of American sidekick, and sometimes takes a true unilateral stance.