Clausy - I actually agree with you re busy roads but until someone is confident out there, I'd stick to the quiet routes (and even if it takes a bit longer - it's much more pleasant on the quieter roads).

As for quickest route to the City- depends where you are in SE23 - I'm down near the old Fire Station on Perry Vale and the quickest route for me is along Brockley Rise and over the Railway Bridge (turn left just after the Brockley Jack) and then along through Nunhead, down to Queens Road Peckham and up the Old Kent Road (I'm off Fleet Street so I head towards Blackfriars when I get to Bricklayers Arms but if you're in the City proper I'd advocate going over Tower Bridge (I used to be based over that way) as I always found the Tower Bridge approach much easier to navigate than London Bridge - I hate coming over London Bridge - easily my least favourite bridge to cross.