You can apply to literally any state school you want in the entire country. Obviously it is sensible to apply to those which your child is able to get to in time for the start time each morning.
After that you need to start looking at the individual admissions for each school, and ensure that you can tick those boxes.
For example, we don't live in London, but wanted DD to go to school there for secondary (she was at a London primary). Because of our address she was unlikely to get any desirable school on the basis of distance.
However, she was very musical, so I spent weeks going through lists of schools to identify all those that had music aptitude places (and indeed any aptitude tests).
Ended up with a big spreadsheet of schools, what they required in terms of criteria for the aptitude test and the travel routes needed to get there. I also visited something ludicrous like 27 schools... which was quite fun but even I was bored of listening to HT speeches by the end. I started looking when DD was in Y5 so by Y6 I took her to see my top choices (worth going alone the first time as DC are often swayed by quite odd things that you would rather they were not!)
A few schools were ridiculously hard to get to, so they came off the list. We then applied to sit the music tests and the banding tests at all the rest. You can do this with as many as you want. You get the results back before the deadline for submitting the CAF so if you are offered an aptitude place it can go in first place and you're not wasting any slots.
For SE London for music, ones worth looking at are: Kingsdale Foundation School (Music & Sport), Co-ed, not religious; Hatcham New Cross Gate (Music), Co-ed, not religious; West London Free (Music), Co-ed, not religious; Prendergast (Music), Girls, not religious; Camden School For Girls (Music), Girls, not religious.
Google and mumsnet are your friends. Worth searching Music Aptitude Test... there used to be some places that coached for the MAT and had a list of schools. (FWIW we didn't coach and not sure it's worth doing).