The "rounded" cocking piece was the "correct' one for early SMLE's, even those built a Lithgow. That specimen is certainly an Enfield product, but there was a fair bit of 'cross-pollination" going on almost from the beginning.
The rounded shape was supposed to "minimise" hand damage during bayonet fighting. Remember that the rifle was seen as a "bayonet extender" that could, occasionally, lower the "tone" of the battlefield and actually be used to fire bullets in the general direction of the enemy.
The "block with grooves" cocking piece was a "temporary" WW1 "relaxation"; much cheaper to make the grasping end.
That "simplified" pattern ended up staying to the end of Oz SMLE building in the mid 1950's.
BOTH patterns were acceptable in repairs / rebuild, as long as they were dimensionally and functionally correct.
The number of Lithgow rifles that ended up buried in French/ Belgian mud, rebuilt in British
arsenals or dumped at sea post war, certainly skews any analysis of production. And then there was the sizeable quantity shipped to Britain, post Dunkirk, during the Second Great Unpleasantness and subsequently lost, rebuilt, "dumped" or "surplussed".
And then there are those like the "J. J. Co" multitudes.