It seems to me that the main difference in the results a school achieves is the "quality" (sorry know that's not the right word, but can't think of another one) of their intake and the parents of those children.
However, whenever someone on here suggests that they'd prefer their kids not to mix with the sportswear clad council house kids, they are universally flamed.
Who then is fuelling the increased demand for houses close to schools that are well away from those children?
BTW I live in a private house, close to a council estate and my DCs go to a school where 40% have free school meals. I have been delighted with the school and it gets decent OFSTEAD reports, but does badly in league tables, which is why there are very few families living in the privately owned "family homes" on this estate and why they are c. 25% cheaper than a similar house in the next town.