The Number 4 Rifle used all BA threads.
BA is British Association. It is a fine thread on a metric standard shank. Thread angle is 47-1/2 degrees.
ENFIELD standard was the very FIRST standardised thread and seems to have been used nowhere else. Sir Joseph Whitworth, the Director at Enfield, developed these into his superior British Standard Fine and British Standard Whitworth threads, both with 55-degree rounded tops and bottoms.
None of them interchange with anything, although BSW and American SAE Coarse are close, sharing the same PITCH but not ANGLE.
But the screws for a Number 4 are FLAT heads, screws for the Number 1 have rounded heads, as pointed out previously. They do not interchange.