The better Universities are still disproportionately attended by kids from the best schools – whether than be public schools or state schools in good neighbourhoods.
I am slightly unconvinced by grammar schools. Cards on the table – I went to one in 70s/80s and it was excellent, best facilities, best teachers. Basically everyone ended up in higher education – or the army – in the days when it was only 10/15% got to go.
The problem is that the system essentially skimmed off that small percent of kids who were doing well at 11 (and 13) – often the kids of professionals who had time to invest (and imagine how much worse that would be now with all those that could afford employing tutors and cramming kids to get them past the 11+), and concentrated the resources on them at the expense of everyone else.
How is that fair on the rest and how does that work in a system where pushing 50% go into higher education? You could argue that 50% gong to uni is too high, but the idea of the policy is to allow us to upskill the economy to compete in high value activity.
That doesn’t mean that the system now is fair – school is determined largely by residence and residence by wealth. So the good schools attract rich people and house prices go up – do you have de facto the same problem as with grammar schools.
I can’t see an easy answer other than putting the extra resources into the poorest areas.