This was being discussed in my office today, and I had to point out that I'm not "British-born" although I class myself as White British as I grew up in Hong Kong when it was a British colony, to British parents (who were born in Britain). However, I didn't emigrate until I was 19, sometime after then handover, so you could class me as an arrival from China. And further to that, my husband is "British-born" and our Polish surname (which causes raised-eyebrows from people who assume we're new arrivals) is a result of his grandfather moving to Britain after the war, when he was released from Auschwitz.
So, one immigrant, one non-British surname, and to meet us you'd assume we grew up locally. Stats are quite clunky.
I'm not sure if the OP was perhaps referring to her perceptions of London, when travelling in, which would include a high number of tourists and commuters who wouldn't be reflected in the survey. Working in London and living in London don't always correlate.