My (unofficial) impression is that it is generally discouraged, but something of a blind eye might be turned for people without their own car for relatively short journeys if the train is otherwise empty.I think you are right. I spoke to a BTP officer at York station and he told me leisure travel was allowed.
Trains are available to all those who cannot work from home and are unable to drive to work.Interesting. How does someone who isn't a key worker but can't work from home get to work then? It's been quite clear in government guidance since the very beginning that you're allowed to travel into work if you can't work from home.
I suppose, one could simply use the argument that they are leaving the station area - by train.