I would send my children to the best school I could get them into, whether that happened to be private or state. And when I say "best school", I mean best in terms of every opportunity it offers the child, and the extent to which it encourages them to take those opportunities, be they academic, extra-curricular or social. Given the current condition of the state sector overall, it looks most likely that it would be a private school.
I don't really agree with the idea of sending my child to an average school with an average demographic, for a "more rounded awareness of society". Obviously there are all sorts of socioeconomic problems occurring outside of the "private school bubble". I wouldn't want my child to be oblivious to this, so I'd explain it to them or point it out from a distance. But I wouldn't want my child to actually grow up amongst those sorts of issues, and experience it day in and day out, to the point where they consider that to be "normal life". If someone at a school starts taking drugs, or gets pregnant, or drops out with no qualifications, I want my child to think "Oh goodness, something seriously went wrong there", not "Yeah and...? What's new?".
I'd rather set the bar as high as possible as to what they should be making of their lives, by surrounding them with, and making them feel more at home amongst the best of society, with people who have done well for themselves. In all honesty, I'm far more interested in having the best for my child, rather than having parity with everyone else.