I am also a UK immigrant. I too have lived here close to 20 years. My husband is British and our children are dual citizens as am I.
Like others on this thread, I enjoy meeting people from other cultures and want to ask about theirs. I agree though that asking people where they are from can be a tricky question, especially recently. A good alternative I've found is asking where they grew up, where they lived before they came to the UK (not always their original country but still interesting) or, in a friendly way, how long they have lived in the UK. Since I have an accent myself, I usually emphasise it in these situations to make it clear that I too am not native born.
That said, even when people are being friendly, it can be tedious to have to explain oneself. My least favourite question is 'Do you miss your home country?' Well of course I do.