Whitworth Rifle Co. Ltd. Manchester, 1860 - 1862 Sales outlet for Joseph Whitworth, sales taken over by Whitworth Rifle co Ltd and other related companies but nothing later that 1886 (British Gunmakers Vol 2 Birmingham, Scotland and the Regions by Nigel Brown)
too early for this rifle

I would hazard a guess that the name was bought? or taken over by possibly a retail outlet who bought this very nice rifle from BSA and had their [famous] name put on it, unless one of the (Joseph) Whitworth companies continued to trade and did the same

TH44