The median price of a house in our state school's catchment is 700-800k. Around 20% of houses in catchment are over a million. The majority of parents are home owners, with very few people living in rented accommodation. The majority of parents have university education. The school has less than 3% of kids on FSM. Etc etc. ...The social mix really isn't very different at our state catchment school than at DC's private school. I suspect that the same would be true at top selective grammars also.
I live in a major UK city that has grammar schools and also a couple of well known independents.
My daughter attended one of the grammars. We have connections with the independents - family friends who taught there, one of the heads was somebody knew, friends of my daughters including her first boyfriend went to the girls and boys independent schools.
It's undoubtedly true that middle-class parents colonise the grammar schools, partly via the ability to pay for coaching. (There's no catchment area.) And that the independent school offers some bursary help - assisted and free places. However, my daughter's friends at her grammar school included people whose parents were civil servants on low pay, cleaners on a low wage etc, a disabled single mum on benefits,as well as those who did well-paid professional jobs.
The one thing that has always stuck in my mind about the girls independent school - which in many ways sounds/sounded lovely - was a friend's account of a sleepover party she hosted for her daughter and daughter's friends (all of who went to the independent). At breakfast she had provided cereals juice, toast and pains au chocolat. And one of the girls looked very sniffy and asked whether either waffles or pancakes could be made available. My friend said she did have other issues with the entitled behaviour of her daughters' friends. I think she mentioned particularly households where both parents were high income and worked for long hours, and had no time to spend with their children - but compensated on buying them a great many of the material goods. Which the children, perhaps naturally began to take for granted. And as they only socialised with other affluent children, they just could not conceive not having designer label clothing etc.
At my daughter's school, though the majority of parents were comfortably off, the well-off children did all know other children who came from less lavish backgrounds.