Oh, TH, that's possibly the least honest description of events I’ve seen?
She didn't "ask a genuine question" she asked successively -
1 “Where are you from?”
2 “No where do you come from?
3 “No, what part of Africa are YOU from?”
4 “Well, you must know where you’re from, I spent time in France. Where are you from?”
5 “No, but what nationality are you?”
6 “No, but where do you really come from, where do your people come from?”
7 “Oh I can see I am going to have a challenge getting you to say where you’re from. When did you first come here?”
8 “Oh, I knew we’d get there in the end, you’re Caribbean?”
Now, I dont care if you think it's racist or not, by the 4th time of asking, it stops being polite and starts being an interrogation.
The 7th question - "where did you first come here?" is after she's been told twice that the other woman was born in London, and the tone of it shows it's no longer polite conversation but demanding.