Yeah, our class system is such a bane. Agree that state systems in other countries far better.
Here though, I think a lot of it depends on the parents tbh. I've known plenty of upper class public school types who thought that saying you were state educated was like saying you went to borstal - these were the snobs whose parents were class snobs and passed on their prejudices. On the whole these "rahs" were boorish and educated beyond the level of their intelligence.
I've also known plenty of nouveau riche send their kids private because they think they are going to get a step up on the social ladder - often these families aren't that academic and their kids aren't particularly better educated than their peers at state schools but little Lily and Jack get to wear their cute little prep school boaters, so that's OK.
But, it is also true that despite the best efforts of some really good teachers, state education has become more and more results driven over the last 20 years, standards have dropped, kids aren't given a broad education, they are taught how to pass exams.
The better independent schools do give a broad education. I'll be sending my DC independent because I'm academically minded, married to an academic, and we believe that the kind of education we got free, on the state, is no longer available. Well, it's available - at a few schools here and there but nowhere near us. We go without holidays and a car and live frugally. We didn't buy the £££ house in the "decent" school catchment area which is attended purely by well off kids, the lower income families couldn't afford to live there, so they are excluded by lack of money from the good states as well as the independents.
If I can at all afford it, I'm not going to send my kids to a school that is in special measures, or a school that is just below the national average in its effectiveness, and I'm certainly not going to do it just to salve my socialist conscience and not appear selfish.
I hope my kids absorb at home a respect for others and I chose the school I did because it doesn't foster that sense of entitlement and social superiority that some of the more "stripey blazer and boater" preps do.
Oh and btw YABU - "indie"? Don't say it myself but it's just an abbreviation, get over it.