To get back to the original question. I had a feeling that we had answered this before. To quote Vanir in 2011
I am not totally convinced. It does seem that the RAF were happy to stick with the .303 because they were convinced by the late 30's that the 20mm cannon was the way to go.
It seems to indicate that all the RAF bigwigs in the late 30's were determined to get the maximum number of bullets fired in 2 seconds rather than worry about the "weight of shot".
Personnally, I think that they should have persevered with the 0.5 over the .303
The thing was that the small Browning was pretty much ready to go. The British did modify to fire open bolt to prevent cooking off rounds with cordite propellent and no doubt would have had to do the same thing with the .50 cal.
Ammo for the .303 was pretty much a done deal, Ball, AP, tracer all existed along with a few specialty items (drill, proof rounds etc) although no one was very happy with the tracer/incendiary.
For the .50 things weren't so cut and dried. There was US ammo but it hadn't been "approved" by the British. Also please note, as has been mentioned before, that US .50 cal ammo in the 20s and 30s had muzzle velocity of about 2500fps. It took a change in propellent to give it the higher velocity that the US used in WW II.
In fact the US .50 cal cartridge had no velocity advantage to speak of over the British/Vickers .5 in machine gun cartridge, it did use heavier bullets.
For perspective here are the muzzle energies of the four rounds.
.303 AP, 174 grain bullet at 2500fps..................2415 ft lbs.
.5 Vickers AP, 580 grain bullet at 2540fps...........8308 ft lbs.
.50 cal AP M1, 750 grain bullet at 2500fps.........10408 ft lbs.
.50 cal AP M2, 710 grain bullet at 2810fps.........12447 ft lbs.
Now the .303 Browning fired just about twice as fast as the .50 cal Browning until some time in 1940. And the big .50 went just about 3 times the weight.
So the British would have had to "persevered" with the .50 by developing higher velocity ammo a the same time the Americans were and also increased the rate of fire of the gun and increased the belt pull.
How much engineering time to you devote to a gun and ammo that the British would only use (on fighters) as an interim gun until they could get the 20mm sorted out?