Rudyard Kipling once wrote that “east is east and west is west and never the twain shall meet.” He could have been talking about fashion in London. This fall, we visited two very different parts of town, and learned where stylish residents go to create their looks. First stop: Broadway Market, in the East End. Once the last leg of a livestock trail to Slaughter Street, it’s now the heart of a cutting-edge gallery scene and a veritable UN of creative types. Next we headed west to posh Mayfair, and spoke with dapper style-setters near the designer souk that is Dover Street Market. We ended our excursion on King’s Road in Chelsea, where both Charles II and Mick Jagger once grooved, and found royally chic Londoners dressed (as Kipling might say) just so.