Windmill, can I ask what schools (primary and secondary) you are talking about?
Mochi, as for primaries, I heard good things about Floreat and Earlsfield Primary, from families who send their kids there. These are families we know and trust so we find that kind of feedback more reliable than that of a stranger on the internet; of course to you I am a stranger on the internet so you should take this with truckloads of salt! We also know another family who is happy with the Swaffield Primary, but that's a bigger school and that can put off some families and kids.
As for state secondaries, the most coveted seems to be Graveney in Tooting; about 1/3 of the places are allocated by merit (performance on the Wandsworth test which all kids attending state primaries in Wandsworth take in their last year) and not by distance.
Other state secondaries are Ashcroft Technology academy on West Hill, Chestnut Grove in Balham, Southfields academy between Southfields and Earslfield.
I'll admit I don't know much about these; Southfields Academy has, for years, accepted all applicants - this alone is usually not a good sign. But they like to stress than, unlike other schools, they don't try to kick out or move elsewhere the worst-performing students to improve the school's test scores.
Ashcroft and Chestnut allocate some places based on specific tests (not distance): Ashcroft measures some kind of technological skills, and Chestnut music and modern languages. I have no idea how these tests work in practice.
The council publishes a list of how places were allocated in past years: https://www.wandsworth.gov.uk/schools-a ... tatistics/
You will notice that some schools allocate places by band: they divide kids by bands based on their results in the Wandsworth test. The theory is that this way classes are more diverse in terms of academic ability, and this reduces the risk of getting classes of mostly top-performing or mostly worst-performing kids. This also means that the maximum distance may be 600m for 1 band and 2 km for another.