Vincent Starrett and H.W. Bell, after walking up and down Baker Street together in 1937, concluded that the house at 111 Baker Street was the "real" 221B. We stood outside that building with some reverence on our recent trip to London. This was after our visit to the Sherlock Holmes Museum down the street, which has been renumbered 221B for commercial purposes.
We also visited the house next to Speedy's Sandwich Bar & Cafe on North Gower Street, the outside of which becomes 221B for the BBC's Sherlock TV series. Except for being on the wrong street, it could pass for the Baker Street abode of our imagination.
Another Vincent -- Vincent Wright of the Illustrious Clients of Indianapolis scion society -- has argued on his Historical Sherlock blog that 23 Baker Street is the real deal. Part of his argument, but only one part, is that 221 adds up to 23 two different says, that is, 22 + 1 = 23 and 2 + 21 = 23. But isn't there actually a third way? What about 2 (2+1)?
So which is the real 221B? None of these. There has ever only been one 221B Baker Street . . . the one that we visit every time we climb with Dr. Watson up those 17 steps to the sitting room he shares (or did) with Mr. Sherlock Holmes. That one's good enough for me. How about you?