I thinknif you've lived in Britain that long most people would think of you as British, especially if you have a reasonably British accent. Where I live in Scotland, most people are happy to accept anyone who actually wants to live in Scotland as Scottish!
Hut there's always going to be racist idiots. I've been told I'm "not really British" just because I'm from Scotland (by someone who obviously doesn't understand the difference between England and Britain. And I've seem the whitest, pure Anglo-Saxon English people being called "not really British" because they wanted to stay in the EU. So, try to ignore the idiots!