Sadly the shop I used to use most (Westend cameras) has become an online-only business, but I also recommend Aperture - their shop that Overrank mentioned (on Rathbone place) is now only a film selling and processing shop and is not open on Sundays. You can see what their film stock is currently likely to be on their website. Aperture also sell 2nd-hand digital/film gear at another shop they recently opened about 5mins walk away (Riding House St).
There are also some other camera shops nearby - Cameraworld on Wells St which stocks new digital, 2nd hand gear and some film; Park Cameras which stocks new digital and some 2nd hand gear (also on Rathbone Place); and Jessops on Oxford St is a chain digital photo shop. One other interesting place just off Oxford St about 10mins away is the Photographers Gallery which has a bookshop and some film as well.
Note if you are buying film that some hand luggage screening lanes at London airports may have introduced the more powerful 3D X-ray scanners that might damage film. I went through one of these at London City Airport last week, but it only seemed to be a single machine in one lane.
Alan