The (symbol)/number stamp is probably a local inspection mark from the manufacturing company. 'swinburn' is the maker - Swinburn and Sons of Birmingham, England. The serial number MAY be their's too as it appears on other Swinburn rifles. It does not appear to have the Birminghan Small Arms roundel on the butt.
The Union acceptance stamp was usually a cartouch with script initials in the stock to the left of the breech. From a quick search:
A "S.L" stamp on the stock of a Pattern 1853 (P53) Enfield rifle-musket, located near the butt plate tang, is typically identified as a Confederate inspection mark or a mark from a private arms dealer/viewer involved in shipping weapons to the Confederacy during the American Civil War.
There are not the 'standard' early acceptance marks (JS/anchor, CH1, etc) which the date would suggest hence my emphasis above.