Agree with most of the above.
I'm in a sort-of-ish similar situation and have looked into the subject a little....
There's definitely good and not so good private schools, so you will need to research them much more carefully than you would a state school. So much more depends on finding the right fit between a school, your child - and your family. I have been adviced to ask the difficult questions (such as "what do you do about recreational drug use") when you have a look around - although obviously use your discretion in HOW you ask! - you will get a lot more insight on how they answer those than the easy questions.
Apparently some private schools are very much more for "media" types and rich/famous families - I have heard that the academic standards leave a lot to be desired in some of these - but you can also see why they would be the schools of choice for some people!
Personally, the one question I would want to find out about is what are the typical occupations of the other parents (i.e. are we going to fit in as a family? Are all the other families going to be holidaying in the Maldives if we prefer to go to Butlins in Bognor? I wouldn't want to send my DC to anywhere they'd be pitied as "the poor kids").
Also, I have been tipped to be wary of the Good Schools Guide, and also take the Inspection Reports (is it ISI or ICI that inspects private schools? I forget just now) with a pinch of salt - as money changes hands between parents and schools, these organisations and guides are far from unbiased, there's a marketing element to them.
The best way is just going to visit them, and observe lessons, behaviour, ask to see their results, ask about discipline, etc.
I have the details of someone who specialises in helping families find schools - she's not cheap but is excellent at what she does. If you (or anyone else!) want details, feel free to PM me!
Phew, that turned into an essay - you can tell I've been off MN for a while!! 