OP, it might be a good idea to update the title and clarify that you're looking for a state school compatible with a 40-minute commute to the City or Canary Wharf.
A few thoughts:
south of the river will be cheaper (unless you go quite far)
Balham: northern line tube, one railway stop from Clapham Junction, Henry Cavendish is a good primary and Chestnut a good secondary
East Dulwich and North Dulwich: Look into the The Charter school and the Charter East Dulwich. Trains to London bridge. Beware that public transport in SE London tends to be not as good as in SW London
Graveney school, near Tooting Broadway (northern line). it is partially selective: some kids get in based on the results in a test, the others by distance. Opinions vary on whether it is worth going there even if you get in by distance only. Kids are divided into groups by ability. One of the largest schools in London - for some it's a plus, for others it's not.
Hurlingham academy: between Parsons green and Wandsworth bridge. No sixth form. Some like it, some say it's too strict (but not crazy like Mossbourne, Ashcroft, Micaela, etc). Houses will be more expensive than south of the river and the commute may be worse