I don't recognise the small class sizes. We looked extensively at all private schools in our area and none of them had class sizes smaller than 22. Some had 26 children, especially the ultra-selective and very popular ones.
If there was a school around with 11 children I would be a bit nervous as to their financial viability, but that's just me beng paranoid. But as there aren't any it is a mute point.
As for wraparound care, all state schools where I live make provision for it (not within the school, but there are companies that work with the school to provide it). Also there are childminders on top who offer a similar service.
So having said all the above, I feel I can't relate to the OP's experience at all - oh and there are no boater hats to be seen, but then again we're UP NORTH so maybe not posh enough to wear them!!!
As for the comment of being above average, frankly as another poster said, if your child is in a decent state school with decent parental support and no special needs then they will be likely to be above average, no need to fork out £10,000 per year in that respect.
Having said that, we have had to supplement/support at home more than I would have liked, but I guess private school parents will be doing that in the guise of homework. One of the criticism of our school is that it sends home no homework thus leaving you with the false sense of security that all is well, when often it isn't. But then every school is different and no school is perfect.