I was privately educated all my school life. I went to a private prep school from age 4 and then a private secondary from age 10.
I can't say it's given me contacts or advantages in life - I'm 26 and have been living at home for two years after being made redundant. I still haven't been able to find another job. I can promise you I made no advantageous contacts at school
I think unless you go to the really top tier schools like Eton and Harrow, the contacts and Old Boys network argument is a bit of a myth.
We've never been rolling in cash as a family. My father worked as an accountant in a regional firm, so although his salary was good, it wasn't astronomical. My dad was the first one in his family to get a degree, and my mum is from a Barnsley mining family... Don't exactly have pedigree bloodlines either!
At private school, I socialised with a wide variety of people. There were uber rich kids there of course, but there were many like me on the less well off end of the scale, there were those who came from very poor backgrounds but were there on scholarships for exceptional talent, we had a whole host of Korean, Chinese, Japanese, African and German kids too. Hell in one or two classes I was the only Brit kid there! Arguably more diverse than the local state school, whose all-white kids all came from the same 5 square miles 
I don't honestly know why my parents sent me to private school. I've heard them say that they looked at state schools before but went with the private prep instead, but I couldn't tell you exactly why. I don't think it was determined from birth that we would be educated privately - I think they just chose the best local school available.