Trivia: In the scene where Saffron is teaching Dougray how to dance at her favorite dance hall, there is a shot of some of the customers sitting and drinking. You'll see Mick Jagger talking to a girl at a table.
Trivia: The twice-used shot of the train rounding a curve is actually near Rabbit Bridge on the Great Central steam railway near Loughborough. The train is in fact heading South; according to the film, it is first heading West (Cambridge to Bletchley), then North (Bletchley to Manchester). The same locomotive is hauling both trains - unlikely - and is suspiciously clean for wartime. However, it was a masterful touch to dub in a passing steam train as background noise when the security man interviewed Jericho in his digs. Such background noise is often conspicuously absent in films.
Chosen answer: This is not a mystery. Claire "stole them to read them" as Tom Jericho told Hester. As he later explained to Wigram, she had taken the messages to give to Puck who had the means to decipher them, and who was looking for his missing brother. The Kestrel traffic from ADU contained the names of victims of the Katyn Massacre. However, Puck and Claire were surprised by the imminent reappearance of Tom, and suddenly fled, explaining why some messages were left behind.