If you look on this website, you can pick which area you want and all the details are given as to whether primary , secondary, state or private, religious faith etc...
http://www.schoolswebdirectory.co.uk/
I hope you find what you are looking for.
I don't know about C of E schools but you can find all Catholic schools, independent, voluntary aided and voluntary controlled in the relevant Dioceses Directory. Westminster, Brentford, Southwark and Arundel will give you a good start! They are listed by Parish.