If there is one thing that my experience living in the UK (having lived in other countries of Northern and Southern Europe) has taught me is that private education as well as non-meritocratic access to higher education are a key component in suppressing social mobility and "keeping people in their place" across generations: in that country the rich and high middle class have this well established path for their children through very expensive private schools (curiously know over there as "public schools", in the same sense of "public" as "anybody can spend a night in the Ritz if they have the £400 to pay for it") and then an "interview" selection process for Oxford and Cambridge where selection criteria are arbitrary such as for example "having attended the right school" (as an aquaintance of mine was told he hadn't, as reason to refuse his application) so that people who popped out of the right vagina and were sent to the "right" (£30k a year+) "public" schools are guaranteed to get in and come out of the other side with a diploma from an "elite" (not quite when it comes to pupils, but definitelly can and do hire some of the best researchers and lecturers) university.

By the way this all continues into their career, since "public" school educated types leverage the connections acquired there (and mommy and daddy's contacts) to literally step into highly paid sinecures purelly on cronyism.

In the UK Education is very much part of a red carpet for life if you were born in the "upper" classes.

My impression there was eventually that, had I been born in the UK to the kind of poor working class parents I was born to, instead of having gone into Physics at Uni thanks to my very high grades at high school and 98% score at the entrance exam (though I ended up switching to and graduating as an EE) and having a successful career across various countries of Europe in Engineering, I would've at best been a car mechanic because the education system in the UK is not at all meritocratic and is designed first and foremost to preserve class membership through the generations.

All this to say that Britain is a perfect example of a very well establish use of private education to maintain the lowest level of social mobility in all of Europe.

PS: Oh, and don't get me started on how "public" schools are "charities" (kid you not!) and thus pay no taxes. It's the very definition of "adding insult to injury" or as they would say over there "really taking the piss out of everybody else".