Not so many these days but recommended labs are Michael Dyer in Endell Street near Covent Garden, (http://www.michaeldyer.co.uk/) and Isis in Farringdon. (Dead Link Removed)
Both just have title pages on these links but if you e mail them they can give you a price and turnround times.
Have fun in London.
Oh, forgot to add, Snappy Snaps (who are everywhere, but there's one on Garrick Street near Covent Garden and one on Wardour Street near Oxford Circus at least) will send it off for a next day service. Never had any real problems with them.
They aren't a pro lab, but there are often knowledgeable people working in there who wouldn't be out of place in a pro lab.