We plan to take the train from York to London on a Friday in June. When I look at a date three months from today, I see all sorts of inexpensive fares, but none of them are available. Is there some sort of trick or a special site at which to get these fares? Do you have to buy the ticket just after midnight British time on the first day these tickets are available?

Cheap fares aren't normally loaded onto website until about a month before. As you are travelling on Friday, a peak travel time, the cheapest fares may not be available.

so to get a sample just put a friday into the site for say a month out and see what is available.

For Fridays try between 4 & 6 weeks. I'd also try to go in the morning as Friday afternoons tend to get booked up very quickly

I wonder if cheap tickets to Edinburgh, where many of these trains end up are more available at about the same price and you just get off in York?