They're separated from the kids round the corner who don't happen to
have as much money.

Actually there were numerous children whose parents were not well off
and who received part or full bursaries at the school attended by my
children. Secondly, there were parents who impoverished themselves in
various ways because they put the welfare of their children and payment
of fees as a higher priority than spending money on themselves or their
house. I think that it's spectacularly wicked that they should have
to do this out of taxed income in addition to paying for a state system
that has failed their children.

What's wrong with all kids going to their local primary school? The
state system will always fail if the bright kids, able teachers, and
pushy parents aren't part of it. The end game with private education is
always social division.