British tank armament policy in the late 1930's and WWII reflected the changing perception of how tanks would fight. The mistaken ideas of the all-tank school, such as Percy Hobart, thought that tanks would be used to fight tanks, so British gun-armed tanks were originally armed with the 2pdr gun, a high-velocity, low-shot weight (as the name implies) piece. Before that, British tanks were primarily armed with the medium velocity 47mm 3pdr. A few tanks (support tanks) were armed with a low-velocity 75mm gun for firing HE rounds. In parallel with the 2pdr gun, there continued to be a small number of support tanks armed with a gun for firing HE rounds. This was not considered to be the primary role of tanks, tanks were to fight other tanks, so they needed an "anti-tank gun". The British bureaucratic mind decided that numbers were more important than quality, so development of the much better 57mm 6pdr gun was deferred so that large numbers of the smaller gun could be producted.
Only after fighting Rommel, who taught them a radically new way to fight, where tanks attacked infantry and emplaced anti-tank guns were used to fight tanks, that the British started to rethink their policy. They also were greatly impressed by the 88mm AA/anti-tank gun, and the power of the larger guns. The organizational infighting in the British army kept the 95mm AA gun from being adapted for anti-tank use during the timeframe when it would have been most useful.
Besides seeing the utility of the 75mm gun on the Pzkw IV, at first a low-velocity gun, when the first American medium tanks arrived, armed with the medium velocity 75mm gun, there was a great impetus to arm British tanks with guns that were suitable for firing at both infantry and tanks. As the 57mm gun started to appear, some were bored out to 75mm, so that they were capable of firing HE. The larger 76.2mm guns that were fairly high velocity only appeared late in the war. There was the 17pdr gun, at first mounted in modified Shermans as the Firefly, and the less bulky "77mm" gun, really a 76.2mm gun, mounted in the Comet cruiser tank. Better guns, such as the potent "20pdr" only appeared post-war.