Can I add to that, the "for profit" private schools are all about the bottom line but there are shades of grey in the private sector.
Firstly, Finton and Hornsby are charities, so they ARE all about the children's education, thats the reason they exist. Its not a coincidence that these schools have such massive waiting lists as they are the best of both worlds.
Next, there are schools such as Broomwood and Thomas' which are for-profit but are family owned. These almost have a matriarch or patriarch approach. You're left in no doubt that they're owned by someone but in these cases (I think) its families and they get a lot back from running good schools, from being the "owners" of the school.
Lastly you have private schools that are backed by investors.
A good example is here:
http://en.wikipedia.org/wiki/Cognita
these guys are a massive education firm backed by private equity
the website of Congitas prviate equity firm is here
http://www.bregalcapital.com/
Bregal exist for ONE reason only, to make money. Thats it. There is NO other reason for a private equity firm to exist. They even pride themselves on the businesses they have sold (its the exit tab) so this is a long winded way of saying its not all bad BY ANY MEANS, but some of it is very very bad.