The problem with trying to preserve the British empire after India leaves is that much of the Imperial holdings had been about protecting India. India had been the jewel in the Imperial crown and besides Malaya the only colony that was directly a direct financial net gain for Britain. Pretty much every other colony was a net drain ( At least in terms of tax revenue. British companies did benefit from captive markets but even factoring that in many of the Colonies were still probably overall financial drains).
Aden colony for instance entire point was to protect the Suez Canal and the sea trade with India. Similarly the Suez canals main purpose was to protect trade with India.
The best the Brits could do Post WW2 was probably keep a few bits and pieces ( Like the way they Kept the Falklands, Girbraltar, Diego Garcia, St. Helena, Ascension, and a handful of islands in the Caribbean.). Malta might be doable. From what I understand the OTL independence referendum actually ended up voting to maintain some sort of status with Britain ( though from what I can recall their was low voter turnout). In OTL the Brits gave them independence anyways. I suppose Singapore might be doable with the right POD. Maybe even Sarawak or Brunei. Belize might also be doable. If the British economy does better and the British space Program actually takes off in any real way I could see the Brits setting up their launch site their similarly to the way the French set up in their remaining South American possessions or the US in Florida.
In order to keep those bits and bobs they'd probably have to copy the French and make them overseas provinces with representation in Parliament.
The problem with keeping even those is that the Postwar British economy sucked. A combination of war damage, the financial and human costs from Two World Wars, over nationalization, trying to quickly build an extensive welfare state, the costs of the post WW2 Colonial Wars, Lend Lease being cut so abruptly, having to build their own nukes and develop and maintain delivery vehicles, and maintaining a large conventional military to potentially fight the Soviets sucked up pretty much every spare pound.
In order to keep those extra bits and bobs you'd need
A) a realistic breakdown over what colonies were retainable.
B) a better British economy
c) A willingness to grant the bits that are kept representation in Parliament and semi full or full British citizenship/ subject status.
Indeed.
Many of the colonies were drains on the empire. The colonies that were drains on the home country were often profitable for some of the big companies doing business there.
These companies profit were in effect subsidised by the taxes payers who paid for the security and admin cost of the colony.
Probably the most expensive colony for its size the British had was Ireland.
After Britain lost its empire living standards for ordinary people in Britain went up.
Qui Bono
You need as the question who benefited for the colonies?
Thomas Paine blamed the land gentry and their system of inheritance.
The land gentry passed on their estates to the firstborn son only. The other son joined the army but only got paid 1/3 pay when not at war.
A war of conquest in the colonies meant full pay and the possibility of a land grant from the crown to set up their own estates in the colonies.
And business those who could get monopolies on imports of luxury good and anything else of value from the colonies.
While the burden of administrating the colonies was paid for by the state.
Colonies had to keep expanding and at some point, the losses of running the colonies became too great. Without the losses in the wars in Europe, this would have taken longer for the burden to become unstainable.