Not to disagree with ringingcod, but every area of SE23 will probably be covered by the catchment area of a school somewhere, but that school might be in on the other side of Forest Hill or Sydenham.
A useful diagram is on http://datacollator.blogspot.co.uk/2013/...lwich.html but it is focused on non-church schools around East Dulwich.
What it shows is that Kilmorie and Turnham Green have massive catchment areas, and so does Haseltine - although not included in this diagram.
However, what most parents want is for their children to go to the local primary state school, especially when they as good as those in SE23.