I also echo what's above. I'm a bloke, but have lived in Honor Oak (i.e. P Rye Park side of One Tree Hill) and then Honor Oak Park (south of the station) for most of the time since 2007.

No incidents in that time, although there was once a gang of teenagers on top of One Tree Hill in the pitch darkness who were interested in my trainers. Until they actually saw them! They never tried anything, I just moved off; the attitude was a little threatening was all.

In general my feeling is that this area is as safe as any in London - you need to keep your wits about you a bit, that's all.