So far the passenger hadn't claimed they had come from station A, only that they required a ticket from that station. One should be cautious, but one hasn't enough information yet.
Instead of revealing the fact that a block is in place, politely ask the passenger where they have traveled from. Could be done quite subtly I expect (the direct question seems rather subtle, confirming the station, and not taking much extra time, but one could also make it as part of the routine a few days before the block takes place). Give the passenger enough rope. The passenger probably won't change their story, and if they do, they then risk doing it the wrong way. For example, a block is on at Burley park, but the passenger decides to try Headingley, since Burley Park is more usually blocked:
Letting the passenger know there is a block on, without them first having confirmed their starting station seems silly. This gives evaders more room to make excuses, and implicitly accuses legitimate customers (the Burley Park example above, or a customer might have another ticket covering part of the journey, but today wishes to travel into the centre instead).
There is a balance to be struck. When I'm purchasing a ticket (although usually before travel) I usually just ask for the ticket I need, rather than provide my whole itinerary. If staff ask for exact details of my intended journey, I will of course be happy to provide them. This seems the best way to communicate things, since my plan is usually then obvious from context. Indeed, previously, when I've given full details of my intentions, I've often found that staff just wish to know what tickets I want (usually because they are then clever enough to fill in the gaps).