I'm in Australia - trying to look up rail prices for either Leeds-London or Manchester-London on 02/01/2023. It's coming up as no fares available. Does that mean sold out, they can't plan that far ahead or user error? Genuinely stumped.
During the Covid pandemic, long distance rail services were made compulsory reservation. Only a few stations were actually able to enforce the compulsory reservations and even that enforcement stopped some time ago, but some operators are still marking their services as reservations compulsory in the timetable data.
Online retailers nearly always insist on generating an itinerary and if the trains in that itinery are marked as "compulsory reservatoin" then they won't sell a ticket against it unless they can make a seat reservation.
Simultaniously a combination of changing covid restrictions, staff absenses due to Covid and now industrial relations issues has thrown timetable planning into disarray. Timetables are being confirmed way later than normal, particularly for weekends, bank holidays etc where engineering works are common. Seat reservations will not be released until the timetable is confirmed.
Unfortunately the backend system that powers rail bookings can't distinguish between a train for which all reservations have sold out, and a train for which no reservations have been released yet. If the rail system was operating normally there would be little need for it to do so, but as mentioned above the current operation of the rail system is far from normal.
BTW as a foreign visitor to the UK, depending on how much travel you plan to do you might want to consider a Britrail pass instead of regular rail tickets.