The 2 second hand vinyl record shops on Hanway Street, W1 ( runs between Oxford Street and Tottenhm Ct Road ) still carry decent stock and if you do go to Record & Tape Exchange Notting Hill Gate (100 yards from the underground station - Cenral Line ), might as well walk the short (ish) distance to Portobello Road to check out Intoxica & Rough Trade ( both good shops IMO ).
Think the replies above just about cover all angles.