One of the three main hilly areas of London, (Highgate and Wimbledon being the others), Dulwich & Crystal Palace have a number of climbs of varying length and pitch to test your legs on.
Claiming Dulwich is good for climbing is a bit misleading to be fair. There’s one primary route up from Dulwich towards Crystal Palace, College Road, other than that there’s no more that I know of.
College Road is a good one though, as it’s a private road with minimal traffic that winds from the grounds of Dulwich College up past Dulwich Wood up to the northern corner of Crystal Palace Park. The climb has three steeper sections, each followed by a short false flat, and the steepest bit still isn’t even double figures.
Crystal Palace on the other hand does have some steep roads, although none of which are very long. Dulwich Paragon CC do a ’29 cols of Crystal Palace’ ride which takes in, surprisingly, 29 of the local slopes. One of these rides is viewable on Strava here.
It’s a place just to go and ride up hills as you see them rather than plan a route, I imagine following a Garmin track round here would be impossible due to the proximity of the climbs and crossovers in the route.
Anerley Hill is a good one to know about as Cadence Performance sits at the top and is one of the best bike shops (and cafes) in London.