With exception of Canadians, "foreign born" in New York means "born at least 2000 miles away" (and thus usually having a different native language and culture). In London, it's "born at least 200 miles away"; usually already speaks English and/or has some ancestry from Britain.
All very subjective, but plenty of people in London who are born 200 or more miles away, "have a different native language and culture", and no ancestry from Britain.
You seem to be saying that proximity of more different countries results in less diversity. Which is odd.
