How did you get on?
If there are 2+ trainloads of passengers on one train, it's not unknown for reservations to be cancelled (which is fair enough) and indeed I am aware of this happening on LNER the other day.
It all worked fine. Maybe because it was quite close between the terminating train getting in and the next one leaving (10 minutes), not everyone went on that one and some waited for the next.
The reservations weren't showing above the seats when we got on, but seemed to refresh at Newcastle where they suddenly showed Edinburgh - London.
The trick (which someone showed us) was that although the LNER site expects you to select a booking reference, you can select "my reference isn't shown" and then just enter anything as the reference and it accepts it