I actually find the "principles" argument against private schools rather strange.
I say that because most people accept, fundamentally, that we live in a society where people have different levels of wealth. We all have our ideas of what size the welfare state should be, how much tax should be paid etc. etc. - but there are very, very few real communists left any more. So basically everything is predicated on an acceptance that, so a greater or lesser extent, there will be rich people and poorer people. Surely a natural corollary of that acceptance is that rich people will spend more money on their kids than poor people.
Now, if we accept that, it seems decidedly curious to claim that they shouldn't spend that money on education. Like, someone earns significantly more than they need to pay the mortgage, eat etc - it's perfectly acceptable to spend that money on plasma TVs, computer games, designer clothes, holidays etc. etc. for their children. But unacceptable to spend in on getting them a smaller class size or appropriate support for their musical ability or whatever, through private schooling.
This makes no sense. Education is a better and MORE worthy thing to give your kids than most of the alternatives. The fact that "not all kids can afford private schooling" is a bizarre argument when we don't apply such thinking to anything else. You don't look at somebody buying their kid something in a shop and say they're a bad parent, because some other kids have parents who can't afford it.
FWIW my two are in state. But we moved to a grammar area and put the oldest through two years of private prep to help ensure 11+ success. So make of my principles what you will. Having taught in both sectors I think there are advantages to each, but the overriding structure of 30 kids per class in state schools is just fundamentally wrong, and should have been ditched years ago. In an ideal world, my choice would be to pay the necessary taxes to bring that down to 20 for everyone, and my experience tells me that that would solve a majority of peoples' misgivings about even some quite "bad" state schools. But sadly, I don't get that choice.