TBH, so much of London is chock full of chain shops!
I'd head to Marylebone High Street (that way you can duck into Selfridges or M&S Marble Arch or any of the other big Oxford Street department stores if you choose) as it's always pleasant and interesting and usually fairly civilised/quiet.
Also might be worth a trip to Upper Street in Islington between the Angel and Highbury Islington tubes - with detours to the side streets especially around the Almeida Theatre - Cross Street is interesting sometimes.
Also might be worth a wander through Primrose Hill, though tbh it's been a long time since I've been, and don't know exactly what's there any more. You'd need to take a bus there probably, as there's no tube stop.
Or, if you take CountessDracula's suggestion of the King's Road - make sure also detour to Chelsea Green. You could also walk up to Fulham Road to have a look around. There's some delicious shopping around Walton Street, but it's frighteningly expensive.
Another idea is to also check out the shops at the various museums. They often have interesting/unusual things that you wouldn't see absolutely everywhere. You could easily walk to the V&A, Science Museum and Natural History Museum from the King's Road.
Have fun!