Litchick - The Old Boy Network is still rife in some aspects of society, in various guises, is the answer to your question.It's not rocket science to work that out. As you acknowledge, it's nothing to do with innate ability, or good teaching, or exam results, since there are hundreds of thousands of children in the upper sets of thousands of state schools who have exactly those things.
This thread has gone off at a bit of a tangent, because some posters are barking up the wrong tree and thinking that the reason a disproportionate number of private school pupils end up in 'top jobs' is because they are more able. Actually, in some respects, Xenia talks a lot of sense here, because at least she realises that she has paid for certain schools for the prestige factor, and not because are children have amazing intelligence or abilities that other children don't.
I don't think things are as bad as some people paint though, and certainly these days, bright children have access to all sorts of interesting and high profile jobs which they didn't in yesteryear - eg medicine (used to be pretty much a closed shop unless daddy was a doctor), law etc etc
Looking at the University destinations for our current 6th form, you'd be hard pushed to know whether it's a state or private school - there's the usual Oxbridge, RG plus other universities.
But yes, I agree, if you are desperate that your child has a good chance of becoming an Archbishop, or a Senior Cabinet Minister, then, yes, you would be better off paying to send them to a private school, which is a pretty abhorrent idea to many people in the 21 st century, and one which many of us don't buy into. Thankfully none of my children aspire to those things anyway, so at least we haven't wasted money on just paying for exam results which they would have achieved anyway!!