If "Lady" is so clearly damned by her own words, why not just copy-n-paste them from the transcript?
Ok - I'll help you out.
Part A: Legitimate Enquiry
Lady SH: “Where are you from?”
Ms Fulani: “Sistah Space.”
SH: “No where do you come from?
Ms Fulani: “We’re based in Hackney.”
SH: “No, what part of Africa are YOU from?”
Ms Fulani: “I don’t know, they didn’t leave any records.”
Part B: Still just about OK, but bordering on racist:
SH: “Well, you must know where you’re from, I spent time in France. Where are you from?”
Ms Fulani: “Here, UK”
Part C: Arguably Racist:
SH: “No but what Nationality are you?”
Ms Fulani: “I am born here and am British.”
Part D: Definitely racist:
SH: “No, but where do you really come from, where do your people come from?”
Ms Fulani: “‘My people’, lady, what is this?”
SH: “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?”
Ms Fulani: “Lady! I am a British national, my parents came here in the 50’s when…”
SH: “Oh, I knew we’d get there in the end, you’re Caribbean!”
Ms Fulani: “No lady, I am of African heritage, Caribbean descent and British nationality.”
SH: “Oh so you’re from….”
The first part above is fine. There is some confusion as Ms Fulani things Lady H is talking about Sistah Space.
Part B is a little persistent but Ms Fulani finally answers the question that Lady H seems to want answered.
Part C is very persistent and overlabouring the question but a definitive answer is confirmed.
Part D is clearly "well you can't be from the UK because you look strange and have a funny name" territory.
I concede that for simplification, I did reword the exchange to make it more Vicki Pollard / Lauren Cooper to emphasise the relentlessness of the repetition of the question as Lady H refuses to accept any answers other than the one she wants to hear.
It is quite possible that Lady H did not intend to be racist or to slight Ms Fulani in any way and that she is merely out of touch and elderly. It doesn't change the fact that this was not appropriate, and perhaps she is not the right person to be doing what she was doing. That said, my grandma was 103 when she passed away this year and she would not have pursued such a line of questioning for so long. Lady H seems to have no self-awareness at all.