Going from my formative years of travelling up to watch EFC away games in London, Chelsea's derbies, if they had any, would have been against Fulham or QPR. Since both clubs had smaller more upmarket fan bases (although I liked Loftus Road) there was never really the kind of derby thing you are talking about.They are in London though.
Chelsea's real London rivalries, I think, would have been West Ham and Millwall, for obvious reasons, plus maybe Spurs as a rival 'glamour club'. (This was in the days of Jimmy Greaves, etc.)