The final episode of the first series, it was recorded on John Lennon's 23rd birthday - 9th October - and hasn't been heard since a repeat in mid-November, almost 60 years ago.
The comedy, a mix of music, sketches and stand-up fronted by legendary Liverpool comic Ken Dodd, would eventually run for more than 50 episodes over six series, concluding in 1968, before the title was used again in 1970 and 1973.
In the recovered episode, The Beatles perform She Loves You. Dodd is also joined by regular support in the form of future Dad's Army star, actor John Laurie; comic actress Patricia Hayes; and Judith Chalmers, amongst others.
Recorded at the time of transmission by late BBC sound engineer and archivist Peter Copeland, it was discovered amidst and digitised from his collection of tapes by their current owner, Ted Kendall, and archivist Keith Wickham, who returned the recording to the BBC.
Do you have any recordings of The Ken Dodd Show or any other old radio or TV series? They may be lost, incomplete, or only surviving in inferior quality. Contact the BBC via its website, or Kaleidoscope regarding material from other television broadcasters.