I second lacb: "Peckham" is the missing link. ("East Dulwich" has crept steadily eastwards throughout the area's gentrification - if you really want to annoy residents of genuine LL + tributaries ED, do it in reverse and call ED "West Peckham" )

I grew up calling the area between Brenchley Gardens and the start of Rye Lane "Peckham Rye" and always thought of the area northwards from Rye Lane as Peckham itself. Because this is so close to the top of the hill, I also used it as the reference for clueless North Londoners, as in "Up the hill from Peckham Rye" Only Fools and Horses and the memory of the mid-80s riots generally ensured that they would then know where I was talking about better than when I mentioned Brixton, Lewisham (blank looks), or Dulwich.