Here is info from Internet Gun Club. Maybe this is the "Charles Smith" you speak of. You might get an idea of the manufacturing date of your gun from the proofmarks and the various times they operated as Charles Smith and Sons.
Charles Smith was recorded as a gun and pistol maker at 86 Weaman Street, Birmingham, from 1861 to 1867. In 1868 he moved to 25 Weaman Street where he was recorded up to 1903.
In 1904 the name of the business changed to Charles Smith & Sons. In 1912 the address of the firm was 25a Weaman Street.
In 1917 the name changed to Smith's Khama Gun Works Ltd, the reason for the inclusion of the word Khama is not known (it may have had something to do with exports to South Africa in particular to Bechuanaland and one of its paramount chiefs who was named Khama 1875-1923).
The name changed again in 1921, this time to Smith's Gunmakers Ltd, but in 1922 a further change was made to Charles Smith & Sons (Gunmakers) Ltd.
In 1927 the company took on additional works premises at 22 1/2 Weaman Street.
In 1933 the name of the business became Arthur Smith, but in 1933 it changed to Charles Smith & Sons. They closed in 1947.
Interesting Daryl! The few C. Smith & Sons guns I have looked over have all been marked with the "Newark on Trent" address! I wonder why there is no mention of the Newark address in the internet gun club descript. Were there two makers with the same name??