Question: 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?

Answer: 
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](https://www.imdb.com/title/tt0120148/goofs/?tab=gf&ref_=tt_trv_gf), which constantly uses American references ("Jeopardy", "Class One drugs") even though it is entirely set in Britain and virtually all the characters are British.
As a term **subway** applies to many passages that occur beneath ("sub") street-level. The Oxford English Dictionary lists three usages that all have the general sense of a tunnel *under* something else:

> 
> 1 a. Chiefly British. An underground tunnel providing access to sewers and other subterranean public utilities, or used to convey water and gas pipes, telegraph wires, etc.
> 
> 
> b. A tunnel (esp. a walkway) beneath a road, river, railway, etc., permitting easy movement from one side to the other. The usual term in North America is tunnel.
> 
> 
> 2 An underground railway. Cf. earlier sub-railway n. 2. The usual term for the underground railways in North America, and for that in Glasgow. Often applied to other similar railways in non-English speaking countries (see quot. 1960), although metro n.2 is also a common designation. Cf. tube n. 7b, underground n. 3.
> 
> 
> 

All three have notes for regional use. In North America, underground passages tend to be tunnels. In the UK, these passages are subways. Meanwhile, underground rail would be called *subway* in most of North America and Glasgow but have specific terms in other places (the London Underground or Tube, the DC Metro, and so on).

It would be unusual to call London's underground rail a *subway* except by analogy. That said, it's possible that person using the tube was from [Glasgow](http://www.spt.co.uk/subway/), that they associated the platform with the underground walkways connecting platforms (of which there are many!) rather than the train platform, or something else semantically consistent but odd usage-wise.