Save as much of the British empire as you can into the present day.
However, you may only describe events happpening after 1945, in other words, the POD cannot be after 1945.
Indeed the weakness of Britain could be a plus since they aren't likely to want to flood countries with troops like the US and Sovs. Countries could be involved in tight military and commercial arrangements with Britain and the Commonwealth as a substitute for empire.
You cannot keep a directly controlled empire after WW2, but you can have a lot of countries as client states of Britain. Indeed the weakness of Britain could be a plus since they aren't likely to want to flood countries with troops like the US and Sovs. Countries could be involved in tight military and commercial arrangements with Britain and the Commonwealth as a substitute for empire.
Keeping some of the island colonies and territories like Mauritius, the Seychelles, Antigua and so on should be rather easy provided that there is the political will to do so. OTL the Seychelles asked for integrated but this was rebuffed by the British government. Malta even had a referendum on its integration into Britain.
Singapore might be doable too with enough political will. Hong Kong requires a treaty of sorts with China.
Perhaps if Suez goes down worse and leads to more of a break between Britain/France and the US, we could see a sort of 'Anglo-Indian' 3rd grouping of ex-British empire states, possibly including Portugal and her colonies, and either including France or allied to a 'Franco-European' grouping in Western Europe.
Malta's referendum only failed on turnout. Apart from small islands, I really can't see this working, not in the climate of the 50's and 60's in the UK. Malta, yes, Gibraltar - of course, Cyprus - maybe (most as the lesser of three weevils), some of the very small islands, maybe. Anywhere with a large and non-white population, sadly no.
Singapore might be doable too with enough political will. Hong Kong requires a treaty of sorts with China.
Perhaps if Suez goes down worse and leads to more of a break between Britain/France and the US, we could see a sort of 'Anglo-Indian' 3rd grouping of ex-British empire states, possibly including Portugal and her colonies, and either including France or allied to a 'Franco-European' grouping in Western Europe.