When travelling around there I always park at Bickley station (next one down from Bromley Sth).
Flashearth link...
http://www.flashearth.com/?lat=51.39....6&r=0&src=msl
Either Southlands Grove or Hawthorne Road have miles of free on-street parking and are about 100 yards from the station.
NB. Bickley station doesn't have ticket barriers and is unstaffed.
Cheers, FP