If you speak Cantonese, are your parents from Hong Kong rather than mainland China? Because obviously the cultures are very different (although possibly converging more as time goes on). If so, I think there are many things that you could be very proud of from your home culture - and I say that as a westerner raising my child in HK, by choice, since I don’t think the UK has anything to offer the young anymore.
It sounds like any thought of “Chinese culture” will remind you of the pain your parents caused, but they are separate things. Their abuse is not a “Chinese tradition” (though I do admit, Chinese parents can be much harder on their kids than westerners, I would imagine because with hundreds of thousands more in the population, everyone has to try harder to get a decent living, so it comes from a place of love, though it seems the opposite and gets taken way too far).
What I can see from living in a culture that is so vastly different from the UK is that the values are still absolutely admirable - for the average person, family is paramount, people are polite and genuinely want to help each other, old people are respected, crime is extremely low, there is no aggression or anger in the way there is in the UK, there is a sense of community - literally, where I live, you could forget your wallet on a table outside (in one of the many community spaces) and it would still be there in the morning, no one would take it.
Clearly there are political issues and massive imbalances of power - but how different is that really from the UK, with the crappy government and the royal family? I saw someone was arrested during the coronation for holding up a blank piece of paper. Not so different then.
I don’t think it is at all unreasonable to give your children fully British names, it will no doubt make their lives much simpler in the UK. But I would hope that you still teach them that they are part of the whole wealth of Chinese history and fable, it is in their blood and they should be proud! Mooncakes, shadow puppets, dragon dances, boat races, mid-Autumn festival, new year, lycee, rich Chinese and Cantonese cuisine, language, art, architecture, textiles, a population that survived a brutal invasion by Japanese forces (again, if HK) - if you can separate your heritage and what you belong to, from your parents’ abuse, you could maybe reclaim it with your children, and be proud of who you are without it causing so much pain?