It turns out that the British had the Projectile Development Establishment at Fort Halstead in Kent under the direction of a scientist Alwyn Crow. These are the guys who developed the various UP AA rockets and should be quite capable of developing a rocket launcher for an anti tank grenade. 

Yep, the technology was all there by 1930,  someone just had to put it together and the leadership had to be receptive to incorporating it.

My alt history country of the period relied heavily on recoilless rifles for both HE and eventually AT work.