The Murder at the Vicarage
All of the episodes take place in the 1950s. "The Murder at the Vicarage" is set in 1954, according to a sign about money being raised for the church fund. This takes place after the events of "The Body in the Library", which Miss Marple relates briefly when describing how she first came across Inspector Slack. "Nemesis" is set in 1955 or 1956 as it is said to be seven or eight years after the murder of the story which happened in 1948, according to the dates on the victim's gravestone. "A Caribbean Mystery" is set prior to this. "At Bertram's Hotel" is set relatively shortly after the launch of ITV (in September 1955), so probably in 1956 (though it also shows the London Hilton completed, which suggests the early 1960s), and "4.50 from Paddington" is set in 1957, during the launch of Sputnik.