And yet everybody who can afford it, sends their kids to private schools in London. Heck - I know people who sold their house so that they could pay for private schools.
The intent usually seems to be to get one's chidren surrounded by primarily middle-or-better class children, not to keep their schooling racially and culturally pure.
I don't think the original post indicated a desire to keep one's children "racially and culturally pure" but rather to avoid sending one's children to schools with large number of non-Whites, for any number of reasons.
It's not a race thing but rather class. People want their children to go to school with отчер kids who are smart / motivated to succeed - hence will focus on school.
Best determinant of that are the parents themselves. So private schools end up being essentially a sieve that checks parents. In the US parents move to the suburbs with high local taxes that fund good schools for the same purpose.