We asked Lewisham whether they facilitate this kind of work and the dutiful Cllr Walton passed on a reply from the Council's Strategic Waste & Environment Manager who said that they can and do:
My team can facilitate community litter picks (we do a health & safety talk too), as well as provide equipment - brushes, litter picks, bags, shovels etc. Colin Sandiford in my team looks after this side of things, but if he's not around then I'd be happy to assist too.
If anyone wants to organise one, please email BC and we will pass on your details to the Council. We may even join in.