The first centerfire gun could not be a Daw as he got the patent from Schneider and a long suite of continental developments by Pauly, Pottet et al.
It may not even be the first British centerfire gun if you look at the Base fire Lancasters (from an original Gastinne design).
The French were providing the thrust of the gun development in the 1850s from Damascus to center fire, breech loader etc.
The British took it from there in the 1860s and made an amazing Engineering effort which was all but finished by 1900.

That being said, it's a wonderful relic from this amazing era...
Best regards,
WC-