Sorry - I meant to say, I have no wish to flame you, personally, but I do take issue with the general demonisation of S London schooling that goes on, and think it not helpful because it does make people scared and nervy, where a visit to a few schools might make them more re-assured! And the good gets tarred with the same generalisation as the bad and people miss opportunities they could have had.
I don't think YOU are a snob, but many decisions to move out are based on snobbery, judging by what I have seen on MN and in the wretched Guardian Family pages (e.g an article a few years ago making wild assumptions about a perfectly sound comp, for example, in which the author faked religion to go elsewhere).
I didn't suggest any of the places I know to have a good location for schools, community and house prices to the OP because it looks as if she would favour N London.
In S London look at living within the catchment for Rosendale and then either Charter or ElmGreen, or any of the E Dulwich primaries and then Charter. Or the Lambeth / Wandsworth catchments for good primaries such as Telferscott and then Chestnut Grove, Tooting for Graveney (or anywhere for the selective places), in Catford Kilmorie is favoured as a primary, good secondary options especially for girls, There are popular primaries in Sydenham or near the Hornimann also with good secondary options for girls (I know less about the boys options, don't know if they exist or not), or in Streatham Hill for Streatham Wells, Hitherfield primary, or Julian's, all for the same secondaries, (Dunraven or Elmgreen) but all with particular catchments, in Brixton Sudbourne or Reay, St Judes for CoE, Corpus Christi for catholics, all excellent schools, as is Ashmole up by the Oval, from which secondary choices include Pimlico or Grey Coat.
These are all schools and routes my NCT ante-natal and tea group families have taken. Doubtless there will be others, I am not a comprehensive expert on state schools in S London! (despite having two children and a step child in the system)
It's tough when you had a bad experience at school. Something I have noticed is that the schools are much stricter now and they are all doing their best to improve both behaviour and results. With mixed success, of course.
Good luck to you, I hope you find the right answer in your search.