Enfield .22 trainer

[Patrick Chadwick]

Was there any time that a peep sight would have been placed on these by the military for training?

I doubt it very, very much.
The purpose of a trainer was to simulate the real rifle at lower cost (e.g. using cheaper ammo, 25 yd indoor ranges). An add-on would have contradicted that intention. So a civilian after-market sight would not have been fitted by the military, and forbidden for military-rules competitions. But trainers were also used by CCF cadets in non-military rules competitions, and could then be fitted with peep sights. The choice would overwhelmingly have been something from one of the Parkers (AG Parker, Parker-Hale) or BSA.

Let alone a Williams?

I would guess that a Williams sight would be a very late add-on by a private citizen, hardly a CCF (not British, y'know!!!), and even less so a military unit.

BTW, there were several different versions of SMLE-based .22 trainers over the decades. Post some pics and we'll find out what you really have!