The thing about the cannon story which has always puzzled me is that the Air Staff had - contrary to many accounts - decided on the 20mm cannon as the weapon they wanted prior to the Battle of Britain; as WW observes, the problem was that the weapons weren't ready for incorporation on the production line, and those which were used in the Battle of Britain were, to some extent, operational trials aircraft. Lessons learned from the experience, the weapons were installed the right way up on the Spitfire IIb and the teardrop fairing on the wing above and below the mechanism was accepted as a necessary consequence (which didn't wreck the Spitfire's performance as some had feared).
Bader was convinced that the cannon's rate of fire was inadequate in fighter versus fighter combat. Tuck (as WW observes) had more information about the efficacy of the weapons and, furthermore, had come to the view from experience that it didn't matter about the rate of fire (Bader's key point) if the rounds hitting the enemy aircraft weren't efficacious enough to do it any serious damage unless you were very lucky. I can't help thinking that Sir Douglas was fighting a rearguard action in a battle he was always going to lose...