I have not been in the financial position to make the choice between state and private, so can only comment on what I know. My daughter went to Addey & Stanhope in New Cross, which at the time was not doing well at all (we preferred Prendergast but she didn't want to go to a single sex school). Despite this, she made lots of friends, has brilliant memories, and got 9 GCSEs. She is now 22 and about to finish a Masters at Goldsmiths.
My son joined Forest Hill Boys last year as we are fortunately in the catchment area to guarantee a place. Their pastoral support has been both essential and brilliant, and several friends speak equally highly of Sydenham Girls.
The point I make is that there's more to it all than just getting great grades; kids have to get through puberty and enjoy themselves too! I am not convinced that the level of pressure in some schools is manageable for every child. I feel that with enough support, they will succeed if they are able regardless of where they are educated.