In terms of what's easy to get to, I think Orc's Nest and L. Cornelissen & Son are really good suggestions. There was or is a general model shop (Gamezone?) within a reasonable walking distance of the same area but it might not be worth the hike to you.
In Cornelissen's, obviously there's a lot of paint you probably won't have any interest in but they have their own line of Kolinsky brushes that are worth trying. This is one of the good shops, where they won't look at you funny if you ask for a glass of water to test the pointing of brushes!
If you might want to look into getting some acrylic mediums, retarder etc. then another good central place to pop into is the London Graphic Centre, which is a short walk from Covent Garden (it's a bit hard to find if you don't have an A-Z but you can always look it up on Google Maps before you go).
And if you happen to make it down to the area of Sloane Square there's another good art shop down there called Green & Stone and ditto all of the above comments related to Cornelissen & Son.
Personally I never go to London without popping into The National Gallery, and the National Portrait Gallery is just behind it so it's easy to hit both in a flying visit. Come to think of it, just up Charing Cross Road a bit is a small art store that seems to have regular sales, right beside the Capital Radio building.
Einion