For harrington jackets try The Merc on Carnaby Street or Sherry's (which is just off Carnaby Street).
There's a Fred Perry shop in London but at the moment I can't remember where it is. One thing I do remember though is that it wasn't cheap.
Have you tried TK Maxx? As they seem to be getting in a lot of Fred Perry & Ben Sherman gear recently. Also they sell the Lonsdale polo shirts which look just like Fred Perry's but have 3 buttons instead of 2.
As for record shops the ones arounds Soho Square are pretty good. Sister Ray does cheap CD's and there's always Daddy Cools for your ska & reggae. Sherry's also have a few mod/punk records & CD's. The Merc also used to sell records but didn't have a lot in last time I was there.