It obviously isn't a .425 WR. Both the proof marks and the straight wall cartridges that I assume purport to fit it indicate a different cartridge. British rifles proved for .425 WR are marked 425EX, not 10.75mmEX, and are Cordite 65, 410 MAX. The .425 is a bottleneck cartridge.
British proof marks from this period for British cartridges weren't in metric. This rifle was built for a European cartridge, not British. The 10.75 rimless comes to mind (347 grain bullet), but the powder charge is wrong and the rifle appears to be chambered for a flanged case, although we don't have a photo from that angle, if the cartridge shown is correct. The 10.75 rimless is also a bottleneck cartridge. Only a chamber cast will suffice.
The T prefix doesn't automatically mean that the gun was made for Westley by someone else. This gun is from 1913/14. The barrels were struck up and signed by Lilley, Westley's best in those days.
