An accurate two second burst from a Spitfire or Hurricane could deliver about 250 rounds on target.
There are always instances of heavily damaged aircraft returning home,just as one lucky shot could bring one down.
The RAF had considered other armament at the same time as the eight .303 option. The then new 20mm Hispano-Suiza cannon was considered "supersensitive" to rigidity of mounting and difficult to mount in aeroplane wings. The RAF would only consider the cannon if 60 rounds per gun,in drums,could be fitted.
In 1938 Dowding wrote to Sholto-Douglas,clearly unimpressed with the cannon.
"There has been a lot of talk about the efficiency of the 20mm cannon and I have seen no proof that this gun will give decisive results.We ought to have carried out the most careful experiments to prove its value before we adopt it.If this was not done I shall wake up in a year's time and be told I am committed to having 15 squadrons of something with a 20mm cannon whereas I can tell you now I do not want any and so perhaps save a large sum of money."
It was not until early 1940 that Dowding was convinced by the 20mm cannon. No.19 Squadron was informed on 1st July 1940 that it was to be equipped with cannon armed Spitfires. They were a disaster,the cannon jamming for a variety of reasons. On 15th July Dowding wrote undiplomatically to the Air Ministry "Two cannon Spitfire unreliable."
The stop gap solution was the 2 cannon and 4 MG armed Spitfire.
There were other problems too,maybe for another thread. As an example the first Spitfire IB to see action with 19 Squadron in October 1940 had to be flown at full power just to keep up with its machine gun armed counterparts.
It's another example of things not being as simple as they appear. "Just" mounting cannon in the wings of the Spitfire eventually led to a modification of the wing spar.
Fighters armed with eight .303 machine guns shot down hundreds of aircraft in the summer of 1940 and that armament cannot therefore be described as "inneffective"
Cheers
Steve