What day of the week are you going? That first bit on the A23 is a bit gritty and motor-ful. The route taken by the FNRTTC may be better (Belgrave square, Sloane square, chelsea bridge, Clapham Common, Tooting Bec, Mitcham, Wallington, Coulsdon Then rejoin your route although getting up on to Farthing Down can be character building as down this way we'd class it as hilly. Take care heading off the other end and over the M25, especially with a touring load on. When you get down to Crawley, consider going east to Turners Hill then heading south via Ardingly, Lindfield, Bedales Hill and Slugwash Lane to rejoin your route.
When are you going?