I believe that Americans would often say 'I ride subway lines'.
I ride the A line several times a week and half of the seats are taken
by people asleep in the mornings.
I ride subway lines to unfamiliar stops and stroll around.
British people would, in general, be less likely to say 'ride the subway'. This is
for two reasons:
As you say, the transitive use of 'ride' (ride the bus, subway, tram, etc) is mainly American. British people are much more likely to say 'use'.
The noun 'subway' means different things to American and British people:
American: an underground railway system in a large city
British: a pedestrian (walking) tunnel usually under a road to allow people on foot to get to the other side without walking in the road.
The only big city in the UK with an extensive underground railway system is London, and that is known as the 'London Underground'. It is also called 'the Tube' because some (not all) of the lines run in round tunnels that look like tubes. People might say 'I ride the Tube (or Underground) to work' and be understood, but they are more likely to say 'I use the Tube (or Underground) to get to work'.
While in London I use the "Tube" all the time.
I visit London frequently and, like most people, I use the Tube to get
around so I'm familiar with a lot of the station
Mr Khan [Mayor of London] said: "When I use the tube, I can't run away from the fact that more were wearing face masks when it was the law"
The only exception to the above is Glasgow, which has one underground railway called 'the Glasgow Subway'.
A common generic term for urban railways, especially those with closely spaced stops and frequent trains is 'metro'.