There is no closer pub to Chelsea, in geography or in history. The Butcher's Hook is the actual room where the club was founded in 1905. The plaque on the wall is real, the location is real, and the matchday atmosphere outside the front door is unmatched.
The founding location of Chelsea FC, with a plaque to prove it. Directly opposite the main Stamford Bridge entrance. Smart interior with proper bar service. Classic London cask ales kept well. A pre-noon pint here is a Chelsea pilgrimage. Members-only on matchdays after midday, so timing matters.
You're drinking in the actual room where the club was born. Plaque on the wall to prove it. Members-only on matchdays, but pre-noon you can usually get in.