Joan Hickson was in an adaptation of this story in 1961 called Murder She Said (1961), Margaret Rutherford played Miss Marple and Hickson played Mrs. Kidder.
The opening scenes feature news reports of Sputnik 1, which was launched on Oct 4, 1957. The novel on which this movie is based was first published in serialized form in a magazine; its first installment appeared Oct 5, 1957.
When Miss Marple goes to meet Lucy for the first time at her club the interior is the same location used for Bertram's Hotel in "At Bertram's Hotel".
The movie is set in 1957 but GWR was no longer in existence as all railways were nationalised in 1947 to become British Railways. The train at the beginning had GWR written on them.
Coincidentally, the main setting for this story is "Rutherford Hall"; between 1961 and 1965 actress Margaret Rutherford played Miss Jane Marple in several productions, including "Murder She Said" (1961), a previous version of this same story.