To reiterate, to the best of my knowledge the work is out to tender, and the contractor will be appointed by the Dulwich Estate after proper, and not unnecessary, consultation with those of us who may end up having to foot (some or all of) the bill.....
However, I think all concerns raised will help in our attempts to urge the Estate get the work done as soon as possible, which they have promised to do. Everyone actually living on Sydenham Rise shares your concerns, believe me!
I don't think your comments about wealth were misplaced, but there is a misunderstanding here about the distinction between the Dulwich Estate and The Scheme of Management and how they operate. I've lived here for 9 years and i'm only just realising now how the whole thing fits together!
I would suggest taking a different route for a while if it bothers you that much, and try to discourage kids from walking along the top of the wall - which is a perennial favourite.
I seriously doubt that Lewisham will get involved apart from asking the Estate to act quickly, which is what we all want.