With the start of the second series, the BBC relented and finally billed the show as “The Goon Show, Featuring Those Crazy People”.

There were 25 episodes, still in the standard music hall variety format of several (usually four) unrelated short sketches separated by musical numbers. The exception was no.8 which had a single plot through the show. This was a parody of Rider Haggard’s ‘She’ entitled ‘Her’, a story which would be reused more than once in later series.
The shows were broadcast on the BBC Home Service on Tuesday evenings between 22nd January and 15th July 1952.
The performers were Spike Milligan, Peter Sellers, Michael Bentine and Harry Secombe. The announcer was Andrew Timothy. The Producer was Dennis Main Wilson.
Scripts were by Spike Milligan and Larry Stephens, edited by Jimmy Grafton.
Incidental music was mostly by Wally Stott, with Arthur Wilkinson and Stanley Black also contributing.
The musical interludes were performed by the Stargazers (first six episodes), the Ray Ellington Quartet, Max Geldray, Harry Secombe and the Goons. The BBC Dance Orchestra was conducted by Stanley Black or Wally Stott, except for one episode which featured the Revue Orchestra conducted by Robert Busby.
The only known recordings from this series are from episodes 1,3 and 25
Synopses of the shows, derived from the scripts, are available here.
We have had access to the original scripts from which these synopses have been derived. Encyclopædia Goonicus has many more details, including the full text of all the scripts.