Episode 10 of the second series was broadcast on 1 April 1952 at 9:45pm. The Radio Times listing is here.
During my research I have stumbled upon a wealth of information available to all. YouTube in particular has hours upon hours of documentaries about the Goons and the individuals involved, as well as uploads of the Telegoons and other TV shows featuring our intrepid heroes.
I aim to share as many as I can, starting with this one: Heroes of Comedy – The Goons.