Brixtons a bit pricey rent wise. I rent my mums place out at £300 PW and I'm a bit cheap on that but they're good tenants so I leave them be.
I would suggest making connections with Pinnoys in the area as they tend to know friends who are looking to sublet rooms.
KCH is not really serviced by the tube so it would be better to be looking somewhere reasonably close but definitely avoid Peckham it should have been bombed years ago.