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: 
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](https://en.wikipedia.org/wiki/Glasgow_Subway) (the world's third oldest) has included 'Subway' in its name at its inception and currently.
There is some confusion here between proper and improper nouns here. "metro" is widely used in Britain is a similar sense the USA to refer an urban railway or train service with frequent trains and stops. "subway" is likely to be understood in it's American sense (metro with a significant underground section) if there is sufficient context to exclude the British sense of a pedestrian tunnel.

A "subway station" could be either an metro station that is underground, or a station on a subway line.

"(the) London Underground", "the Underground", and "the Tube" are proper nouns and refer to an organisation (currently part of Transport for London, part of the London government) and the railways and train services it runs. "tube" may also refer to the small diameter trains and tunnels used on some London Underground lines.

"the London metro" is undefined, except for the Docklands Light Railway there is no set of railway lines with stops closer together, High Speed 1 is the only dedicated express line which not next to a metro line. See an [old geographical](https://www.whatdotheyknow.com/request/224813/response/560395/attach/3/London%20Connections%20Map.pdf) map or the [current plan](http://content.tfl.gov.uk/london-rail-and-tube-services-map.pdf). Compare with [Paris](https://www.ratp.fr/sites/default/files/plans-lignes/Plans-essentiels/Plan-Metro.1555581459.pdf), [Brussels](http://www.stib-mivb.be/irj/go/km/docs/WEBSITE_RES/Attachments/Network/Plan/Net_Reseau/Plan_Metro_Train_1902.pdf), [Hamburg](https://www.hvv.de/resource/blob/3204/d713455052fa2510b3f9cc5ee938c0ac/hvv-usar-plan-data.pdf), [New York](http://stewartmader.com/subwaynynj/) and [Washington DC](https://upload.wikimedia.org/wikipedia/commons/0/00/Washington_Metro_diagram_sb.svg).

Since London has no metro, can it have a subway? Possibly, but there are railway lines outside of London Underground with significant underground sections including the East London Line (since 2010), Elizabeth Line (under construction) and Waterloo & City Line (before 1995).

In summary, you can call many London Underground and some non-London Underground station "subway stations", but London Underground is not the "London Subway" and is definitely not the metro.

The reason the journeys in central London often involve the Underground, is that it and the Thameslink route are the only railways that cross central London.