IMHO, ’White’, ‘Black’ etc are terms rooted in nonsensical ‘race’ theory. We all have different colouring: skin, hair, eyes and genetic features (like red curly hair or brown eyes). So, IMHO saying ‘non-White’ is a nonsense. Who does that in include? People with a sun-tan? However, some people identify as ‘White’, ‘Black’ or ‘Brown’ and that should be respected.
Official nationality is UK. That’s what it says on passports. Lots of UK nationals weren’t born in UK (e.g. because their parents lived/worked abroad at the time). Lots of non-UK nationals were born in UK (because their parents lived/worked there at the time). Lots of people have dual nationality, e.g. both an Irish and UK passport.
There’s no such thing as ethnically English. Because the English are from many different ethnic backgrounds, e.g. Celt, Viking, Anglo-Saxon, Norman, Castilian, Romany, Arab, Indo-Aryan, Punjabi, Sylheti, Somali, Yoruba etc etc. Lots of different ethnicities arrived in England when it was part of the Roman Empire (which was vast) and due to the British Empire (which was also vast). And due to its many seaports, e.g. Somali sailors in the 1800s.
People who live in England may or may not consider themselves English. It depends. For example, they may consider themselves Irish, Scottish, Welsh, French, Jamaican, Nigerian, Pakistani etc etc. Or a combination. It’s a matter for them.
Cultural and ethnic heritage is usually passed on. IMHO, that’s a good thing. For example, a person born of Catholic parents from Lancashire (but who was born and lives in Essex) may still be proud of/celebrate, their Catholic and Lancastrian heritage (practicing certain traditions (like fasting during lent) or eating certain foods (like Lancashire Hotpot or barm cakes). They may, in addition, be of Polish heritage, and celebrate those cultural traditions (like eating pierogi). People with a US parent (of any colouring) may eat turkey on Thanksgiving. They’re still English.