SE London is a large area, ranging from SE18 (Woolwich) towards the eastern part to Camberwell (SE5) and Walworth (SE17) more west. If you are able to travel to Wallington Girl's School (OK not co-ed, but if you need boys (!), there are Wilson's AND Wallington Boys nearby), it is brilliant. If you are capable of getting A*s, you should be able to pass their entrance exam.
I have advised transfer of two of my students from private schools to Wallington and they have excelled (one is now final year medical student at Brighton Uni).
(Specialist A Level Biology Tutor)