I’ve done London -> Dorking on the A24, and I seem to remember it the A24 is not that bad once you’re out of Dorking / motorbike idiot territory (ie. past Leatherhead.) Even in that bit, you just have to cope with them whooshing past at ridiculous speeds.
A3 is not desperately bad either – you’re going into London, you hit Elephant and Castle, which is a pain, but unless you go super early, you’ll be going faster than the cars anyway. Proper London playing with cars it’ll be.
Although pulling into London after Clapham Common, going along the embankment will give you a bit more of a nice London ride – Chelsea Embankment etc. are lovely to whoosh along on a road bike.
Personally I’d try the direct route first, and then mess around with it if the cars are slowing you down too much, or if you don’t like the big junctions.
Joe