I mean, I completely empathize with their situation, but the fact of the matter is that the UK has even less of a claim to governance over the territory than China does. It’s physically connected to mainland China with no other countries or territories around.

The fact that the situation is unfair to HK citizens doesn’t have much relation to the fact that there’s no legitimate reason for the UK to have any involvement at this point in time, unless you’re just plain and simple in favor of imperialism.

In that case you’d be making the argument that people who more closely align with China who live in North Dakota are allowed to just vote and declare North Dakota to be a Chinese province.

There’s a whole spectrum of diplomatic measures that the UK can do that make zero difference in the situation.

Trade restrictions? The UK fully depends on Chinese imports. It would hurt the UK more than China.

Recognition of Taiwan? What would that change? Western countries already defacto recognize Taiwan and work with them as a close ally. This would be changing vocabulary on some documents and plaques.