I'm sure it is true. I go to a relatively minor public school, but I know the odd person at schools like Eton, Harrow etc and they really do come from families which are well known in certain circles and the family background intself carries clout. Whether they are let in purely because of that, who knows but I think is unlikely, but for some in certainly is a factor in acceptance.
The person above saying they'd be "discredited" - quite the opposite. Why would there be headlines, loads of organisaitons and elite educational organisations aswell do partially work like this. For example, on my application form for my school, it actually asks for relatives who have connections to the school or who have been there. Family connections still play a huge part in Britain, and personally I think a touch of it is a great thing.