One thing that I did think of early this morning is that the British (and everyone else in reality) went along with what they had early in the war. The Brits had the .303 Browning, the 20mm Hispano and really nothing in between until they adopted the .50 Browning (early versions weren't that great and the UK didn't have the ammo in the production or supply chain as far as being common until later).
Interestingly, Rolls-Royce tried to design a HMG for the RAF. The Wikipedia article (not sure how accurate it is, though it sites a source published by Rolls-Royce Heritage Trust) does suggest that the weapon was intended to fire .50 BMG, as the RAF wanted a weapon similarly powerful to the AN/M2 .50, but built in Britain. The original recoil operated weapon had functioning issues, and was redesigned to be a gas operated weapon. There was also plans to use the .55 Boys AT rifle round in a rebarreled version.
In the end, Rolls-Royce gave up on it (and a 40mm cannon they were working on) to concentrate on aircraft engine production.
Interestingly, Rolls-Royce did license production of a version of the 40mm cannon to another British company for armament on Royal Navy motor gun boats.
Many countries used what they had and then progressed to what they were planning/developing before the war. It often took 3-6 years to bring a gun from initial concept to working squadron service. This last is somewhat debatable as the US .50 was supposed to have been used for pretty much all of the 1930s and yet it didn't work for the British in 1940 and early 1941 for the British is several different aircraft. The German MG 131 and the MG 151 were both in development in late 30s.
You also have to tool up a factory to make the guns and another factory to make the ammunition. Or buy the ammo from an other country. And you have to print the training manuals and train the armorers before you try to issue the guns to service squadrons.
Britain wanted a 2nd source for a .50 cal Machine gun, however, as these things often do, certain people just didn't want to copy the existing weapon, they wanted "improvements".
Like a shorter, lighter weapon that was more suitable for turret installation. As a note here, the US made under 8,000 50 cal guns in 1940 so there weren't enough to go around for the US Army, the US Navy, the US Air Corp and the British. Things improved by an order of magnitude by late 1941 and in 1942 they were cranking out well over 100,000 a year.
The RR gun cut the barrel by 5in which helped with size and weight but that increased muzzle flash so they had to put a sizeable flash hider on it which pretty much canceled the shorter length. The RR gun was supposed to fire faster but it never completed development so who knows? The gun, according to one source, was supposed to weigh 49lbs, The receiver was made of a proprietary RR alloy, which may or may not have affected production at a later date. One source gives a rather low velocity, but since the British were using the M1 Loading with a velocity of 2500fps in 1940-41 cutting the barrel shorter may have cut the number to the value given?
Changing to the .55 Boys seems to be an unneeded complication although it may simply have overlapped the progress of the US .50 cal ammo.
By the time the RR machine gun was under development they had cut the weight of the .55 Boys bullet to increase the velocity and the resulting bullet weight and velocity wasn't much different than the .50 cal M2 load (and it's variations).
But for the British in late 1941 or early 1942, they don't have a factory set up, they are not set up to make ammo in machine gun quantities, not AT rifle quantities. US .50s are showing up in numbers, and aircraft designers (or least fighter designers) are figuring out 4-6 gun 20mm planes and the gun designers are figuring out faster firing 20mm guns.
As far as the RR 40mm gun goes. There seems to be a large difference of opinion between the Wiki site and another reputable source (Mr. Williams), It seems to have been not as good as the Vickers S gun and later in timing. The touted use on MTB/MGBs as an AA gun needs a little explanation. As a gun against enemy small craft it may have been quite useful. As an AA gun? The thing weighed about 3 times as much as an Oerlikon and was mounted on the same pedestal. It fired semi-automatically (gun fired and ejected the spent cartridge and then remained open until the loader rammed the next round into the breech at which point the breechblock slammed shut) in this mode the gun fired at about 30rpm at best instead of the 114rpm (?) of the magazine fed aircraft gun. You could shoot it at airplane and it may have been marginally more effective than the boat crew simultaneously raising a one finger solute to the attacking plane but not much. It may have been better for morale.
The 40mm gun went through BA to BH versions (with a few skips) and the BH versions received 4 mark numbers, there seems to be no information on the MK III and the MK IV was belt fed after the magazine fed MK I & II.
