Both Hawkers and Supermarine put forward 20mm cannon armed versions of the Hurricane and the Spitfire. This was in response to the specification F.37/35, (the same specification that resulted in the Whirlwind) orders for prototypes were issued to both companies and then cancelled (Someone at the Air Ministry decided that a single engine fighter could not carry four 20mm cannons. But of course the Defiant could carry the drag and weight of a turret) About two years later both companies were instructed to fit cannons to there respective aircraft. Therefore it is a racing certainty that if the Orders to Supermarine and Hawkers to Specification F.37/35 had been left alone there would have been at least some effective 20mm armed RAF fighters in the BoB. The Air Ministry Strikes Again!
I often agree with you - but not here. Yes, Hawker & Supermarine put forward designs for this Spec. but these were quickly cast aside due to them wanted to concentrate on their current production aircraft orders, and wanting to look at other new designs.
Hence, two aircraft were ordered from Boulton-Paul P.88a (Hercules) and P.88b (Vulture), a twin from Supermarine, and two from Westland. Sadly the Treasury, wouldn't provide the funds for so many - hence only the Whirlwind for that Spec. Moreover, you'll see from that - no problem with single-seat cannon fighters, but nb both P.88s had higher h.p. engines than the Merlin.