The thing is, people just don't seem to use the term "English" in this context. So, for example, you have people saying "British Asians" or "Black British", but never, so far as I have ever heard, never "English Asians" or Black English". It's not logical.

If you ask people in England their nationality, regardless of their ethnic background, it's a toss-up whether they say "I'm English" or "I'm British". Assuming they were either/both.

"English identity" is not a straightforward thing.