According to Cooley & Newton's book
Cogswell & Harrison, two centuries of gunmaking, C&H occupied 226 Strand from 1882 to 1928, and 168 Piccadilly from 1917 to 1982. The years the two addresses overlapped were 1917 to 1928, and I would assume your gun was made during that time.
Cogswell & Harrison today has the old C&H archives; check
http://www.cogswell.co.uk/archive.htm# For $50 or so they will look up your gun and provide a Certificate of Origin, including when and where it was built, and for whom, original specifications and selling price. Pretty interesting stuff which I found well worth the money.