I live in Sydenham and ride in 2-3 times a week and this is the route which works for me.
Straight up Westwood Hill, right at the top down Fountain Drive past Dulwich College. Straight over past the picture gallery to Dulwich Village. Left down Burbage Road and past Herne Hill Velodrome to Herne Hill. Follow Railton Road through to Brixton and take A23 North (lots of traffic lights but also a bus lane to hide in.)
Even on a bike you’ll get snarled up in rush hour traffic through Brixton and Railton Road keeps you out of that mostly.
I turn off the A23 at Kennington to go over Westminster Bridge but you should keep heading North. If you head for St Barts hospital there’s some quiet streets through Smithfields to get you to Farringdon.
Re Crystal Palace Hill – hard to avoid it, but it’s great training! and you do get used to it. Alternatives are go through Crystal Palace Park – then you meander up the hill rather than straight up which is easier and traffic free. Or go from Sydenham across to Forest Hill and join the South Circular up to East Dulwich. There’s still a climb but not so brutal. A lot more traffic though.
On the way home when you reverse this route you’ll get to do College Road – listed here as a classic European climb 🙂
Guardian link