I haven’t spent much time in London, and the two times I have been there, shopping was the last thing on my mind.  That being said, I was big on street style those days, so Dover Street Market was somewhat of an accidental pleasure (just kind of wandered in there).  Of course, if you’re looking for some fine tailoring, there’s always The Row, which is a whole different animal in and of itself for which you should probably head over to Style Forum for some advice.  Sorry I couldn’t be of more assistance.