new infantry 2 Pounder and the smoke/HE job could be done with the existing mountain howitzer so would not finance the putative 6 Pounder so the design lay on the shelf
Not sure where this comes from.
British tank guns on the prewar years a complete mess, and they certainly did spend a lot of money for very little results.
The existing 3.7in Mountain howitzer was never used in a tank.
There was a 3.7in howtzer/mortar used in the A9/A10 and some A 13 cruiser tanks.
The shell was 10 1/2 lbs according to one source and the max range was around 2000yds, MV was about 620fps (189m/s) and chances of hitting a point target at ranges long than a Webley pistol could shoot were dim. It only weighed about 222lbs so it balanced in the 2pdr mount fairly well. HE shells were rare, one source claims only about 4 rounds out of the total but sometimes they didn't have even that.
This was replaced by the much more famous (or infamous) 3in howitzer which took over the Smoke/HE role. While the shell was just over 13lbs the velocity only increased a little bit and the range did not increase by more than 500 yds.
The 3.7in mountain gun barrel and Breech was about 451lbs. Won't fit in a 2pdr mount. And launching 20lb projectiles out the muzzle at the upper charge levels is going to break something fairly soo.
Nobody was making smoke shells in the 6pdr (57mm) caliber, You can't fit in enough chemical to make it worth while. You need to got to about 75mm to get smoke.
The mountain guns were NOT general issue infantry guns. They were used by special units. The 3in stokes mortars could fire smoke for the infantry for local support and the artillery (18pdrs and 25pdrs) where supposed to handle all the normal artillery support.
Now somebody is going to come up with the 2in mortar and smoke shells. They existed, they were used, but at short range for very specific targets and actually a lot of them were used for signaling, not creating sizable smoke screens.
Now the army and the bean counters should have been providing HE shells for the AT guns and tank guns from the start. A lot of men died because they didn't.
Anybody else that made artillery had figured out how to do it.