That would be a good question for Peter Laidler, I have a feeling these stamps were not base level inspections and were done by a higher level. Under the American system you have base, intermediate and depot level inspections so I think the rifles were inspected by someone from a higher command.
I have 13 dvds full of manuals from the MOD Pattern Room Library on British weapons and equipment and I concentrated my reading to base level repairs and upkeep of the Enfield rifle. At one time I had the largest and only Enfield manual sticky at Gunboards but now everything is at milsurps.com so check your sticky " Lee Enfield On-line Knowledge Libraries (Index of Articles)" for information.
