Sorry to add to the muddle, but I went down the rabbit hole because of the proof stamps on the floor plate. I thought it may have originally been barreled/chambered for the 375 Flanged Nitro-Express (right charge, wrong bullet weight), and came up with this from Imperial War Museums - ROSS MODEL 1903 SPORTING RIFLE .370 EXPRESS:

Ross Model 1903 sporting rifle .370 Express | Imperial War Museums

The upper hand guard has no place on a commercial sporting rifle.