+1 for adding a single mile to go through Richmond Park. I would go up Coombe Ln, left into Warren Rd, into the park at Laddersill (sp?) Gate, down Broomfield Hill, to Roehampton Gate, Priory Ln, Upper Richmond Rd, Bolan Bridge, Lower Richmond Rd, Putney Bridge, Right towards Hurlingham Park, Straight across at the very end (by PC World), Imperial Wharf, Lotts Rd, CS8,Whitehall, Traf Sq>
Isn't Warren Road a private road? Are you allowed to cycle down it? I was going to go that way for a journey once but re-routed just incase.