There was some documented 'experiments' regarding the ability of machine guns to shoot down bombers - you know the one that would always get through
Anyhow - the Brits rigged up 4 then 8 machine guns and came to the conclusion that even with the 1150 RPM of the .303 Browning MkII air gun 1000s of hits (4500 was the figure given) were required to reliably down a given twin engined bomber
And the Spitfire with 350 rounds per gun (2,800 rounds) - could deliver the lot in just under 20 seconds - so unlikely to down a bomber in one pass
The weight penalty of the .50 HMG and its ammo was not thought worth the small improvement that it would provide and with 4 guns replacing 8 and with a much reduced ROF again
The HS 404 20mm on the other hand while initially badly managed - ie the long barrel was for cowl mounted weapons but the British simply ported it into a wing mounted system and a delay in buying the design - did deliver a marked improvement on damage and despite issues with the gun it went on to almost totally replace the Browning MkII .303.
Once those issues were resolved by mid war most British aircraft carried 2* or 4 cannon
*The thin wing of the Spitfire made mounting and heating of the outer 2 guns problematic and in general only the inboard mountings were used limiting the Spitfire to 2 Cannon and 4 MMGs (or 2 HMGs)
However the myth of the .50 cal is very likely a result of the US completely ignoring the hard won experience of the British in getting the weapon to work as a wing mounted air gun and instead spending the entire war trying to fix issues the British had already fixed in 41/42
Due to the issues in getting the US M1 and M2 weapon to work reliably the British did not use the US supplied weapons and the US soldiered on with 4 or 6 M2 .50 cals in the majority of their fighters
http://quarryhs.co.uk/US404.htm
So I find that in forum discussions US members dislike the 'unreliable' 20mm Cannon while the British think they were the best thing since slice bread - the main reason being that they are really discussing 2 different weapons.
So with regards to the OPs question - I think for the BoB the British should have tried harder to get the 20mm to work as it was know for some years that Rifle calibre Machine guns simply didn't cut it any more
The use of the Mk 108 might seem foolish given its weight, low ROF and ammo supply but when you consider the damage it caused to 4 engine bombers from a single hit - it does make sense
Perhaps a mixed armament - 4 lighter cannon for Air to Air (not to be recommended in a ME 262) and 2 Mk108s but with a greater ammo supply per gun although you then run into problems with the sights etc due to the differing trajectories