Currently, the only people that can send their children to independent schools are those that can afford to pay high school fees on top of their taxes. This means that independent schools perform less an education function - although they receive almost universally better results than their nearest state school - than a signaling function. Go to a private school, and you're showing off that you can. That's grossly perverted.

But we can bridge the divide. Allow a diversity of schools by type in the public sector - including those that select on the grounds of ability if the local parents want it, like the school I went to. We also need to give parents real control over where they send their children. We need to enable all parents with the purchasing power to take their children out of the local state school if it can't meet their demands, and into an independent school that does. That way, we can make all schools work for the parents, and introduce real pressure on both state schools and independent schools to bridge the gap and heal that wound in our society.