It is worth bearing in mind that this area, along with the Rec, is Honor Oak Park. Would make a great site for a market garden IMO but regardless, unless robustly challenged, Southwark will continue to nibble away at this until there is none left. That would be a sad loss for future generations IMO.
Even if you buy the contentious idea that yet more burial space is needed, am struggling to see how public access is enhanced by this proposal. The current access from Honor Oak Park road remains the same, pedestrians, often with children, have to walk on the access road to gain entry and go through a car park to get to the Rec/Swings. There are also big drainage and biodiversity issues and no evidence has been supplied on how these are being addressed.