LNER said it expected its east coast main line trains between Scotland and London on 23 December – the first day of the five-day festive travel window – to sell out quickly when tickets go on sale on Friday.
Extra trains will be laid on but seat reservations will remain compulsory.
Seat capacity has been halved to comply with 1m social distancing.
Upgrading work on the east coast route will also disrupt trains from Christmas Eve, with no services in or out of London King’s Cross from 27-30 December.
There will also be no trains on Christmas Day or Boxing Day, as normal.
An LNER spokesperson said: “To support our customers this Christmas, we are increasing services from early December up until the planned disruption begins on 24 December and are continuing to operate reservation-only services to prevent overcrowding.
"LNER is running as many services as possible up until planned engineering work on 24 December.
"There will be a reduced timetable on 24 December.
"Services ahead of Christmas Eve are expected to sell out quickly.
"We urge customers to plan ahead this Christmas to avoid disappointment.
"Services are likely be very busy from 31 December to 3 January due to substantially-reduced services into and out of King's Cross.”
Avanti West Coast said its services throughout the 23-27 December travel period were “highly likely to be exceptionally busy”.
Its tickets and timetables will be available from Tuesday.
Hourly services will operate between Glasgow and London and every two hours between Edinburgh and London via the West Midlands.
Trains will finish earlier than normal on 24 December and start later on 27 December.
The operator warned that the east coast line works were likely to mean its trains on the Glasgow-London west coast route would be busier than usual.
An Avanti spokesperson said: “With reduced capacity to maintain social distancing onboard, we strongly advise customers make a reservation to travel on their preferred train.”
However, all fares would be switched to off-peak from 18 December.
ScotRail said it did not anticipate any major increase in travel during the reduced restrictions period.
Tickets will be available from early next month.