Ok, from the map posted by Ghis, it would seem that the One Tree Hill area and the top of Devonshire Road are Honor Oak and from the station to the other side of Stillness is Honor Oak Park.

Honor Oak Park Estate is definitely in Brockley! (they can have it!).

What do you call that bit that goes from the top of Wood Vale to the start of Peckham Rye? Its official name is Forest Hill Road and it contains the Forest Hill Tavern.....