(in the context of travelling to London from Yorkshire for work, at least once a week)
For a day trip, ring customer and say `sorry, trains messed up, are you busy tomorrow`. London based visitors seem very understanding of this. It doesn't work if you've a hotel booked. But I have previously phoned hotels and explained and they've changed a pre-booked room for free.
Tickets valid next day is a useful option, and if even some people take it up then less congestion.
For stuck in London coming home. Given a choice between
- `hang round station and hope` or
- `travel a different route` or
- `phone round London friends, go to pub, sleep on their floor, get first train home in the morning, argue if they claim I'm in peak on an off peak/advance ticket`.
I'd put `pub` on my first choice of options. And I've done this.
I've done `travel a different route` when desperate. It can go very well, east coast dead so travel west coast and TPE and arrive 2 minutes earlier than I planned to.
Or it can go badly: sitting on the floor of a rammed East Midlands train, with 15 other people also in the vestibule and a small child using my bag as a seat. (didn't mind child on my bag) That's an experience I'd prefer not to repeat, but I was kind of desperate.
I suppose the real solution is balancing relative capacity of the services. If London to Sheffield was every half an hour, with a decent length train, there would less packing if one of the other 2 mess up. If there was also a decent Cross Country service from Birmingham - Sheffield - Leeds - York.