Gino, it's not an accuracy problem, per se...
It was a case of what's called "Wandering Zero".
The guns will group just fine, if you use good quality ammo. (Isn't that always the case, folks get some surplus offloaded on purpose by a foreign government and try to shoot sub-MOA?)
Supposedly, the weight reduction efforts that differentiate the No4Mk1 from the No5Mk1 Lee-Enfield removed so much metal that the gun couldn't maintain it's zero between shooting sessions.
Depending on who you ask, it's either a problem or a non-issue.
My own No5Mk1 had a horrible action/forend/handguard fit, it fairly rattled. I glass-bedded it, clearanced the forend and handguard, and have been quite pleased with the gun's performance, and zero-holding ability, ever since.
Now, another thing that may indeed influence the gun's "zero" is the fact that the shooter develops quite a flinch from running a full battle cartridge in such a lightweight carbine. This ain't an M1 carbine round, or a 7.62x39. It's a .303 British, running a 174-180gr bullet well over 2400 fps. Newton's laws still apply, boys and girls!