I teach quite a lot of 1st/2nd/3rd/whatever generation immigrants, from (off the top of my head) Bangladesh, Romania, Hong Kong, Nepal, Czechoslovakia, Poland. Probably more too, but we don’t tend to notice the white immigrants once they’ve lost their accent.
As I said on another thread, most of us will have a non-UK ancestor in our relatively recent past. I’ve an Irish surname, though that’s from a good few generations back, and I’m as Italian as I am Irish because that particular immigrant married an Italian dancer. I’m more Scottish, with a maternal grandad born in Scotland, but that didn’t stop my sister who moved up their getting grief off a woman on the train because she was Scottish.
As Stewart Lee observed, the current ‘scary’ lot of immigrants from Bulgaria and Romania are just the successors to those from Poland, Pakistan, the West Indies, the Irish, …, Anglo-Saxons, Beaker folk, Neanderthals, fish coming over here and forming an integral part of our life, society, diet and culture.