It's stated to be 1952 at the beginning of the show, but the letters retrieved by Tuppence from the kitchen waste bin are stamped with brown stamps bearing the portrait of Queen Elizabeth the Second. In 1952 George VI was still the King of England, and stamps bearing his portrait would definitely have been used.
However, Queen's reign started in early 1952, and as it is not stated which month events take place, stamps with Elizabeth II's portrait being used isn't error.
A Morris Minor Estate Wagon ("Woody") is shown several times. This is supposed to be 1952, but these did not appear until October, 1953.
Incorrectly regarded as a goof. Whilst it is set in 1952 Elizabeth II commenced her reign in early February 1952 and a set of stamps was issued with the Queen's image that year. We don't know what time in 1952 the story is set so it is possible and more likely that year for Queen Elizabeth II stamps to be used.