2Lbr's had HE rounds. It was used for certain in 1941, I've got a first hand account where the gunner specifically states he used HE rounds as the solid shot was too good, and over penetrating. I think they existed earlier than that, I'll have to make enquiries. Granted the early HE was a little bit light on Bang, but that happens when you've got a superb Atk gun, bit like what happened with the 17lbr.
We didn't lack Atk performance either. Name me one tank in 1940 service that the 2pdr couldn't put a hole through? There for a delay was perfectly sensible. I mean yes, it'd be a great opportunity to jump ahead a bit and get everyone a 6pdr in 40-41. But it was hardly a desperate need.
Also calling it a pop-gun (As
@robinrocket111 did) is a bit of a lie. Again what is the normal calibre of tank guns in the period?