Here's something for those who feel impulsive and like to make travel decisions on the day. Virgin Trains East Coast (VTEC) are rolling out advance tickets that can be purchased up to 2 hours before departure. Over time advance purchase tickets have moved from being available up to a week before departure, to 18:00 the day before and then 23:59 the day before. Those booking travel on the day were restricted to the walk-up fares even if they were happy restricting themselves to a particular train.
CrossCountry have offered advance tickets on the day for a while now, it's easier for them to do as they have electronic reservations on all their trains and although I knew VTEC were wanting to do similar I was surprised they rolled it out before the electronic reservation systems on their Azuma trains were available. Currently advance tickets are available on the day only between London and stations towards Leeds and the cut off point is two hours before departure. Departures before 10:00 are excluded and the T&Cs say available on selected journeys, this is presumably to cover for situations where it's not possible to reserve the train two hours before (e.g. if the train has already set off from its starting station there's no way to add reservations to a moving train until the Azuma brings electronic reservations).
Is this good news? Presumably Virgin Trains East Coast want to encourage people who need to travel at short notice to consider the train, it can be considered as one of the methods they can use to encourage people away from their cars. I expect prices will be set in a way to discourage people away from the busiest trains meaning those that can travel at slightly incovenient times will be rewarded with larger savings than they could currently get if booking on the day. Of course, the further you book in advance the lower your fares will be (unless you're unlucky and they hold a sale after you've booked) but if a meeting comes up at short notice or you just fancied a day in Leeds these tickets can help save you money.
Even if it turns out these tickets don't work for you the prices for the walk-up fares have not changed so this just gives additional options.