The great dilemma of all 20th Century British wanks. To make the British Empire last, India has to be integrated into the political system, British MP in the House of Commons in large numbers. But even with a very rigged voting system, India is an important voting block on day 1 and with a generation or two, India number of MP is so large that MP from the British Isles matter little.
Hang on. Since when does being a 'Hyperpower' require you to be a single united nation, or have a cabinent representing every element of it...
Hyperpower, means a power that;
"A power that leads all other power in every sphere of endevour."
A hyperpower doesn't need to represent it population, it just needs to be world leader across the board. To that end, India can be treated like dirt but so long as it is working nomilly for the British, then the Brits can claim dominon on India and make India part of its Geopolitics. Indeed this even extends cross nation in some respects.
If we look at
America or Russia they are both essentially federations, with local government and a federal government. While this has become the dominating system of these two powers it is not the only political system in place. Both China and India practice their own forms of 'federation'.
What the British Empire might represent is a 4th way of forming Hegamony, not by national borders, but commonwealth identity. So long as all the elements within the Empire are acting 'for Queen and country' it doesn't matter one jot whos in the local and colonial governments about the world.
In that sense a British Empire that never collaspes, that keeps its colonies allied to the crown with nominal soverignty (i.e. the right to local governance, but Britian retains the right to represent them at the intenational level (something that could fairly easly be sold to people under the guise of Britian vouching to protect their interests))
and you get what is know as
a Confederation.
...Hence since there is no prerequsite for a hyperpower to be a single state
per se and it might be possible for Britian to actually reform the Empire in the 20thC rather than desolve it, you could possibly get Britian becoming a defacto hyperpower because it simply encompases so much of the world under its 'Commonwealth'.
Indeed this 'Commonwealth' would not just be a sociopolitical one, but a geopolitical one. Rather than uniteing people of common cause, it unites nations under a common banner.