No-one makes .360 centrefire shotgun cartridges any more to my knowledge. They are very much collectors items. There was the .360 No.5 Rook Rifle and .380 Rook Rifle rounds that were made in shot versions; I have some in my collection but they will be about 100 years old.
What make is the gun? And what do the proof marks say? This could be a rare and valuable item. If it is .360 shotgun, I would suspect that it is likely to have been black powder proofed only. All the bolt action ones like the Webley were for the 9mm. rimfire also called the No.3 bore Garden Gun. Fiocchi and Hirtenberger are about the only people who make them any more. Any newish Eley 9mm. stuff is likely to be by Fiocchi.
I suspect it should be easy to make ammo for it by sizing down some sort of pistol case. Photos of proof marks may help to solve the mystery. Lagopus.....
