My teenage daughters loved the RickSteves recommendation for shopping on the Left Bank in Paris -Sevres-Babylone to St. Sulpice. The shops were small, unique, and actually affordable. This year we are going to London. Any similarly hip but not-outrageous priced boutique areas? We know about the street markets and we will mostly avoid the top-end designers and dept. stores. Has Carnaby Street been reborn? Is Kings' Road dead?
I was not impressed with Carnaby Street, but I think the Covent Garden area has many wonderful shops, in the actual "garden" and among the many surrounding stores. I like the "Accessories" store there.
The Camden Lock Market is the place to go for trendy fashions in London. Its open everyday, but much more lively on the weekends. www.camdenlock.net
Kings Road is where your daughters would want to shop. There are lots of small unique shops there.
There are lots of small streets in Chelsea that has neat shops, Ellis Street and elizaveth Street. They probably would enjoy Covent Garden also. In the Portobello area try Ladbroke Grove and Golbrone Road.
Covent Garden and Camden Locks are the places to try. Also the Greenwich market on Sundays. Covent Garden changes every day, so check it often. You might also want to check out the market in Old St. John's church yard off Picadilly.