If I was the UK, in such a scenario - I'd probably be pushing for Taiwan and something geographically convenient that contains the entire Pearl River Watershed. We've seen how that region IOTL exploded economically - but that entire region being Hong-Kong-ified or made into British China would be able to allow the British to exert power throughout the Pacific. I'd also very rapidly be trying to find someone else to rule it in the long-term. Essentially make the area an investors dream. Free China as the financial investors party-land. Huge investment profits to be made to sell goods in China from Free China, and a large domestic market. Further, as a British Protectorate/Dominion, if Hong Kong and Taiwan are still under direct control, you've got the potential for the British to have logistics across the Pacific as well as across the Indian Ocean, which would be powerful strategically.
It'd be interesting to see a TL where an Industrialised South China intervenes in Northern China eventually, or whether it would at all, if the idea of a unified China can be broken.