Yeap!
This is the study, or small living room if you like, of the supposedly small appartment, or better put suit, that Sherlock Holmes and Dr Watson were occupying in 221B Baker Steet in London! As I can recall they had to renumber all the buildings in the street to make this appear as the place where the famous detective lived.
No, they just changed the number on the museum building. It sits between 237 and 241, so should really be 239 Baker Street by the tradition of London street numbering.
The Museum is a fiction, just as the character of Sherlock Holmes is. He never lived, and there was never any 221b in Baker Street. The klicky is a fatbelly, and Sherlock Holmes was not fat in the stories, so attaching this moniker to the figure is suitably fictitious, which is what I though Alex might be getting at.
From the original stories, I think the museum's rooms are too far small, nicely appointed though they are, but the museum's creators were limited by which building was available and affordable. Until 2002 a branch of the Abbey National Building Society stood on the site of 221 Baker Street, but in 2002 they left and the site started redevelopment into an apartment block.
There is a far more likely house on which Conan Doyle based his stories further down on the other side of Baker Street, which you can see the facade anytime, and is noted in a self-guided Sherlock Holmes Walk that I did in the Summer of 2009 when I knew my time in London was limited.