All the lovely hills!
I find the A233 hard work on the bike. It would be a lovely road if it weren't for the the traffic. The problem I find is that it is easy to carry speed, up to the limit even in some of the 40mph areas, but even traveling at the same speed as general traffic it's a very difficult road to maintain road position. There's often too much width to be able to control overtaking vehicles but frequently insufficient room to allow comfortable passage side by side. I've sat in primary along stretches of this road and slowly been bumped back ten or fifteen cars as I've had to ease off as each driver pulls alongside and then inserts themselves into the gap I'm maintaining in front of me. Mentally tiring and physically harder work too.
The local driving mentality is also why I wouldn't necessarily recommend the lanes that by-pass Biggin Hill. In the rush hours otherwise quiet country roads are used as rat-runs by people looking to make quick progress despite blind corners and general narrowness. Layhams Road and particularly Fairchilds Road are worth being wary of which is a shame as they both by-pass New Addington which is somewhere I'm told you should never go on a bike unless armed.
Despite what I've said, as a ride that I'd be able to roll along as un-interrupted by traffic lights as possible my route would be: Clark's Lane; Beddlestead Lane; Skid Hill Lane; Layhams Road through West Wickham to Eden Park Road and Elmers End to filter through all the traffic to begin the ascent of Anerley Hill. Taking the route down College Road and Croxted Road to Herne Hill can result in a long fast stretch as long as the traffic isn't completely ballsed up. There would be another bout of creative filtering as you approach Brockwell Park before what is usually a very clear run along Railton Road and Atlantic Road to emerge on to the A23. This route from Crystal Palace and then running up through Brixton and on to Kennington and Baylis Roads I find to be the swiftest if noticeably longer journey than the alternative through Dulwich, Denmark Hill, the Walworth Road and the Elephant and Castle. The downside of this route though would be the ups - it's stupid hilly, though it might make a nice occasional ride in. That's probably the best aspect of your journey - you probably have enough decent options to ride a different route each day of the week, possibly a different route home each day too.