However, the RN's FAA always emphasised firing time in their purpose built aircraft so the decision for 6 guns in the F4F-4 is interesting, since a 6 gun Martlet was wanted by the FAA.
I have never gotten a good answer on this although I have mentioned it a number of times.
The FAA didn't get the Martlets
when they ordered them. And the .50 cal M2 specifications changed in 1940/41 and the ammo changed in 1940/41 although more for the Americans than for the British.
Martlet Is delivered in 1940 (fixed wing, Wright engines) probably had 600rpm guns (at best) and 2500rpm ammo. They were ordered in Oct 1939 by the French and may have been ordered with French guns?
Data card says 300rpg and there are errors on the data cards. Since these are ex-French aircraft we can also not assume that they are direct equivalents of the F4F-3. This leaves us with a few questions.
At the moment I can't find the order date for the Martlet IIs. First one flew in Oct 1940 but was not delivered to the British until March. Different engine than the Martlet I. Only 10 built with fixed wings in March/April (?) and then the pause in production until the they got the folding wing. Did the folding wing and fixed wing get different number of guns?
The 30 Martlet IIIs with fixed wings are delivered in the spring of 1941.
Now the .50 cal guns that were being delivered in the P-40 Tomahawks were, shall we say, less than reliable (at times unusable). Did the RN ask for the 6 guns to make up for the unreliability? Did they ask for them because of the low rate of fire? four guns times 780rpg (13rps) is 52 rounds per second vs 40 rps (at best) from the 1940 ear guns or 60 rps from six 1940 era guns. I can understand if the British made their decision based off those numbers but I don't know that they did.
The US boosted the velocity of the .50 cal ammo from 2500fps to over 2800 fps in late 1940 or early 1941. British ammo contracts didn't change specifications at this time. British were ordering 2500fps ammo for some time after the US changed (British may have gotten the US spec ammo lend lease).
The British did revert back to the four gun armament for the Wildcat V (Eastern Aircraft FM-1/F4F-4) in 1943. And the Wildcat VI (FM-2 with Wright engine) But these would have had the faster firing guns (around 800rpm).
Also do not compare the .50 cal guns in the Mustang in 1943/44 to the .50 cal guns in the Wildcats in 1940-41-42 because the US was slow to get incendiary ammo manufactured and issued. British may have had some but it didn't exist in 1940. The US used a large amount of M8 API (incendiary filler in front of the AP core) from 1943 on but it wasn't available in 1940. Mustangs were getting kills in 1944 with ammo the British didn't have (and didn't know was coming) in 1940-41. It was also ammo that the USN didn't have in 1942.
There can be a number of reasons that the British asked for 6 guns in the Martlet in 1940 and all of them seem to be good reasons. I don't know what the actual reason/s were.