I don’t get your pictures in super good quality on my phone screen, but the barrel shenanigans are not reflected in the British proofs that I can see.
The gun has the Enfield acceptance stamp on the left side, the markings on the rear frame plus the crossed pennant proof in front of the cylinder; these belong together and were applied when the gun entered service.
The NOT ENGLISH MAKE and the nitro proofs on the right side of the barrel are early commercial proofs applied after retirement and before the gun could be sold commercially; they are pre-1955, as the NOT ENGLISH MAKE was eliminated that year.
PS: Just realize I never addressed you question. Yes, I think it’s a New Service shipped to Britain likely during WW I. If I read the serial correctly as 122695, that would put it in 1916.