By Bad Seed
This is the theme for "The Adventures of Sherlock Holmes" (with Jeremy Brett). It is called "221B Baker Street", and was composed by Patrick Gowers. This particular version I obtained from "The Return of Sherlock Holmes" DVD Collection. It is one of my favorite pieces from one of the best television shows of all time.
P.S. Here's the song in HQ MP3 format: http://www.megaupload.com/?d=Z6SYL1YQ