King's Cross Station, London
King's Cross railway station is a major London railway terminus, opened in 1852. It is on the northern edge of central London, at the junction of Euston Road and York Way. Some of its most important long-distance destinations are Leeds, Newcastle and Edinburgh.
The 39 Steps (1935)
The train shown leaving Kings Cross in the film is the LNER Class A3 locomotive "Trigo" (#2595), which entered service in February 1930 and was withdrawn in November 1964. As with the other A3 class locomotives, it was named after a famous racehorse.
However, the train shown exiting the tunnel as the Hannay's landlady discovers the dead body of Miss Annabella Smith isn't the "Trigo", nor is it even on the same route — the train is a Great Western locomotive exiting Box Tunnel near Bath.