Updated: Oct 12, 2021
The second episode of the second series of the Goon Show was broadcast on 29 January 1952 at 9:30pm on the BBC Home Service. Don't believe me? You swine. It's right here in the Radio Times, page 26.
I'm still working on my own mini-bio of Sir Harry Secombe, aka Neddie Seagoon, so for the interim period, here's a lovely documentary about him made after his death in 2001.
I enjoyed the remark early on about his voice bringing people to tears - in the second series the BBC tried to ban him from singing at all.
Captain (Sellers): Can you see them? Seagoon: Yes! Yes, there they are, clinging for dear life to that gramophone record of Harry Secombe singing "On with the Motley". Moriarty: Help, throw us a gramophone, or it'll be too late.
(from 'The Lost Year', Series 6 Episode 13, broadcast 13 December 1955)