I thought this might come in handy – here’s a map.
(click to get to the Google Map).
The green area is Eliot Pits where the playground is planned.
The blue is Heathside and Lethbridge, an estate being redeveloped without a play area. See the architects plans here.
The orange is the big flat space of land mentioned in Kate B’s comment.
I’ve no idea whether it is available or not, but it seems to me that there are plenty of urban areas in Lewisham which would benefit from a playground. If the Blackheath Society define themselves as Guardians of the Heath, that’s a tricky role to live up to, whilst attempting to please everyone in the area. It seems this proposal may have been a step in the wrong direction.