Train on Bank Holiday Questions (York > London)

That's broadly correct, but operators do tend to choose bank holidays to do engineering works, so you can't necessarily assume all trains will run as normal. You'll just have to wait until closer to the date to see what the schedule is.

Look out for an off-peak ticket - this will allow you to travel on any service on a bank holiday, rather than one specific service.

Train tickets don't sell out - if all seats are taken people juat end up standing, but coming from a major station like York that's very unlikely.

That is NOT correct. On a main line it is a normal weekday schedule if there is no engineering work. On London commuter routes they have a Sunday schedule, but that is the only city where that happens.
Anywhere else it is a weekday schedule. That means 3 trains per hour from York to London.
Effectively a walk up schedule, with the last one at 11pm, arriving in London at after 1am.
This is the normal timetable- https://assets.ctfassets.net/mxack5k9p2sw/4raBidSw46xiLx10c2ci0S/2b989dafa4d13f9361cec33c2b845068/LNER_Dec_2025_May_2026_Timetable_Guide_Web.pdf
Trains in the UK cannot sell out, if no seats are left then you stand but there are always tickets available.
While prices do rise there are almost always Advance (train specific) fares available until 2 minutes before departure, so it is very unlikely that you will ever pay full fare.
As an example it is now 0741 Saturday, there are £39.80 fares on the 0830, and as low as £23.60 on the 0931 this morning. Fares on all trains today are between those points. This is quite normal.

Thanks for your correction isn31C, and apologies juleeem for misadvising you!