I did the reverse (but started in Wimbledon) and found the A31 very busy with lots of slip roads to cross with high speed traffic.
Doing it again, I go to Basingstoke via Picket Piece, Whitchurch, Overton. A30 to Blackwater then frimley, B311 A319 to Chobham, ottershaw, Chertsey, Walton, Kingston on Thames, Twickenham, Brentford and on to Chiswick