"...only ammo that shoots well..." Good. It means the headspace is likely ok, but have it checked anyway. Thousands of Lee-Enfields, of both models, were assembled out of parts bins with zero QC.
Headspace is a rifle manufacturing tolerance that allows any maker's ammo to be used in any like chambered firearm. If it's too large, the cartridge comes back upon firing and causes the bolt to be hard to open. Among other things. Hard extraction, flattened primers, et al. The absolute worst case is the locking lugs on the bolt breaking sending the bolt into your head. Relax. That rarely happens.
Fixing bad headspace is easy. You change bolt heads using headspace guages until you find one that keeps the bolt from closing on a No-Go guage. It's not inexpensive with a No. 1. You need a handful of bolt heads at $22.00 each to try with the guages.
Take it to a smithy. You'll have to find one who has the guages though.