Liberty!! Gotta go to Liberty - it is wonderful and the accessories are second to none. Bill Amberg has great bags - classic but stylish. I'd also put in a vote for Pickett on Sloane Street for some classic British style, Vivienne Westwood for some edgy British eccentricity. If you subscribe to the dailycandylondon newsletter you will get the heads up about all the sample sales in town, many of which will be bags and shoes. I'd also suggest browsing along Marylebone High Street and Portobello Road - the latter is great for Vintage. Don't overlook Covent Garden either - brilliant boutiques carrying a range of luxury goods and unusual designers especially in Monmouth Street. Bicester Village is only a hour and a half from London too - lots of discount stores there including Anya Hindmarch, Mulberry, Chloe, Celine, Dior etc.
I'll stop here, but PM me if you want to discuss further - I could go on and on!!