The screenplay was not based on any published Agatha Christie story. It did, however, borrow a few obscure plot details from "They Do It With Mirrors" and there is a delightful moment when Miss Marple pays homage to Christie's long-running play, "The Mousetrap."
The novel central to the plot, J. Plantaganet Corby's "The Doom Box", was devised by the scriptwriters and never really existed. The prop-makers mocked up copies in both hardback (for the Battledore) and paperback (for Miss Marple).
We see Miss Marple's impressive library. It is composed mainly of Pan and Penguin crime paperbacks (including duplicate editions of "Follow the Saint" by Leslie Charteris and Georgette Heyer's "The Foundling"; Edgar Wallace is another of her favourite authors) alongside crossword, quiz and limerick books, Noel Coward's "Pomp and Circumstance" and "Return to Peyton Place" by Grace Metalious. There are also copies of Agatha Christie's "Three Act Tragedy", "Appointment With Death" - and intriguingly, the Miss Marple short story anthology "The Thirteen Problems".
Some of the film takes place on Trafalgar Day, partly dating the events to October 21st (the anniversary of Lord Horatio Nelson's death onboard HMS Victory), an important date in the British Naval calendar.
Miss Marple's recently-deceased uncle was Rear Admiral Sir Hubert Marple; her grandfather Sir Bertram Marple (Admiral of the Fleet) founded The Cape of Good Hope Youth Reclamation Centre and its training ship the Battledore.