Using "subway" as name for London Underground?
Here in America, I was taught in the mid-60s by disc jockeys playing the Petula Clark song that in the UK "subway" means a pedestrian tunnel beneath a street, not an urban rail transit system. But on today's rerun of "The Saint", an episode set in London, a character with a British accent says to Mr. Templar, "She committed suicide. She stepped off a subway platform right in front of a train." This episode is in color, meaning it was made around 1968-69.
So can subway be used for the Tube as well?
Solution 1:
Your understanding of the different uses of "subway' are correct. In the UK it means a passage (usually walkway) beneath something, often a street.
However with internationally marketed entertainment a different dynamic often comes into play. Whereas British audiences would mostly have understood the meaning of Americanisms, even in 1969, it was generally assumed that US audiences would not have understood the meaning of Britishisms, even if they were used in a strictly British context. Such shows often take the decision to use the American terminology even when it is illogical to do so.
For an extreme example consider the movie Sliding Doors, which constantly uses American references ("Jeopardy", "Class One drugs") even though it is entirely set in Britain and virtually all the characters are British.
Solution 2:
I cannot account for The Saint, but as a native of England I would find it very strange to hear another of my countryfolk refer the London Underground system as the subway. It would almost always be referred to as the Underground or the Tube.
Take the underground for two stops, but be quick as the tube station closes early on weekends.
Subway in the UK tends to refer, as you say, to a path underground typically beneath a busy road system. Also referred to as a pedestrian underpass, with footbridges over busy roads often called a pedestrian overpass as an antonym.
If you don't want to cross through the traffic there is a subway you can use, or there's the overpass if you don't mind heights.
Solution 3:
The author of the Saint novels, while not being American did live in the states for most of the period that he was producing the books, so it is possible that the particular usage you have picked up bled into the author's vocabulary during that time.
Leslie Charteris was born in Singapore to a Chinese father and English mother. He was educated in the north of England and briefly at Cambridge before moving to the US where he spent most of the rest of his life, so his familiarity with the niceties of the usage in regard to the London underground may have been limited by lack of exposure.
Of course, the line may be attributable to a script writer rather than Charteris, but even within the UK at that time the distinction between 'Underground' and 'subway' was, to an extent, peculiar to the London Underground. Glasgow's underground railway (the world's third oldest) has included 'Subway' in its name at its inception and currently.