Camden is often recommended as a great place to look for clothing. Unfortunately, some of the market areas have either been demolished (in readiness for redevelopment) or damaged by fire and many of the websites about the area are seriously out of date. So this link should be regarded solely as an indication of the variety of outlets that Camden offers, rather than as recommending any specific shops, or market stalls, (which might no longer exist):
http://www.camdenlock.net/fashion/alternative. html
(Nearest Tube stations: Camden Town & Chalk Farm)
Although Carnaby Street (and the surrounding area) is mainly remembered for its impact on fashion in the 1960s, I was recently pleasantly surprised to note that there still seem to plenty of independent (often 'quirky') clothes shops around there. (Nearet Tube station: Oxford Circus)
For some wonderful shops, selling the type of clothes you're looking for, forget London and jump on a train to Brighton. The North Laine area has plenty to offer you.
Chris
PS: Disclaimer - This post is from a guy in his mid-50's who freely admits that he knows sweet F A about fashion! ;-)