I think if you're looking for good value, or even good vintage watches, the bricks and mortar retailers in London are not the place to go.
You're typically looking at things being sold at over twice what you could find them for on forums, on eBay, or through private sellers on instagram - and often the items on sale are tailored to the "oh man I want something old but I want it super shiny, please polish it for me" level of taste.
If you wanted to spend a morning or afternoon looking at brand new stuff, and then some really overpriced vintage, and then a mega store of all the modern shinies, the Bond street boutiques (Omega, Breguet, JLC, Vacheron, Patek, Breitling, Rolex... I'm sure there are more I'm missing) followed by Burlington arcade, and then Watches of Switzerland on Regents street would be a good shout... and keep you in a fairly self contained area.
If you want a bit more of a horology/culture hit, the Clockmaking exhibition at the Science Museum is fun, as is the Royal Observatory at Greenwich.
Enjoy your trip.
