I think EDT have jazz nights once a month - might be worth asking there. Also further afield, you could approach Pizza Express who have jazz in some of their branches and the Savoy cocktail bar.
I am terribly old and have no idea where the Peckham Bowl is but there is a skate park in the top part of Peckham Rye Park. On a street map, Homestall Road entrance is the nearest.
Shhh, Macroban - don't let the cat out of the bag. It's a tunnel to the wicked delights of McDonalds, KFC, Subway, etc on Rye Lane (as the blessed Ms Spark hinted at in "The Ballad of Peckham Rye").