Why do the Bren Mk3 and Bren MkII rear sights have the same part number?

Because it's mounted very slightly higher? That's only a guess on my part but the same principle works (? after a fashion.....) on the No4Tyards/L42metres sight

But the Mk3 Bren wasn't designed for the longer ranges and I seem to recall that its accuracy due to the light barrel was marginal at over 800 (?) yards in any case but that's what you get with a lighter Bren barrel. Another point was that the length and weight of the Mk3 (and 4) gun barrel was critical in order to achieve the best compromise.

They quickly found out that while the barrel was being lightened in stages during the Pendine trials, it was a grave mistake to make the muzzle section (past the gas block) lighter by reducing the diameter because this caused the bullets to scatter wildly. IT could only be shortened and even then, any shorter than it is will cause an unacceptable amount of lack of gas stoppages

Good question and there'll be a lot more answers I'm sure