It's on the boundary of Southwark/Lewisham councils so you may see Southwark employees/vehicles around. Perhaps that particular estate is within Southwark.

So far as Peckham being a 'dangerous' place, it is a gross generalisation. It covers a fairly wide area with some lovely houses along the Rye which for the most part is considered an extension to East Dulwich. The Peckham that gets the worst press tends to be north Peckham.

Babaloo - come with an open mind. You may find local kids in a park (the horror of it - why aren't they sitting in front of their Xbox ) but that doesn't mean they're going to cause you problems. There are lots of great green spaces around here (Horniman Gardens, Peckham Rye, Dulwich Park, Sydenham Woods as well as Brenchley Gardens) that you'll find lots of local residents using - running, cycling, using the outdoor gyms as well as reading/chilling/walking dogs.

There are far more good people here than dodgy ones. Good luck with your move.