Well, there is Austin Kaye on The Strand, Watches of Switzerland on Oxford Street have a small collection of used watches and Burlington Arcade (seriously high prices)
For brand new - Harrods, Selfridges' Wonder Room, Jura Watches on Burlington Gardens. Just around the corner from there is the flagship stores of both Rolex and Omega. Wempe is walking distance from there heading back twds Bond Street.
That is just off the top of my head and I'm not local to London, but I'm sure that some of our other members will add some more suggestions.
Have a good trip - hope you have good weather 8)