+1 to what bcmatt said.
Last year the HEX operated a replacement bus service - twice an hour I think - from LHR to central London; can't remember if the GEX offered a replacement service at all. Car services, eg
Just,
Simply,
Handicars and
Addison Lee will be operating from LHR to central London on 25 December but rates usually rise by 50% on that day.
The 0845 and 0945 departures from London Euston to Lancaster show availability in F for just £48 (£60 for the 1045 departure) on 26 December - with a single in Standard at £56

for those services. Manchester to Lancaster has singles from £6.50 on the 26th.
If you fly to London for an arrival on the 25th then you can either take the HEX rail replacement bus to central London, book a car service or pay for an airport hotel. If you want the convenience of door to door services with your bags then book a car. The
Travelodge at Euston - and it's no more than a one minute walk from the hotel's entrance to the entrance of the rail station - has rooms on offer for 25 December at £32.
It's not the smartest hotel in London but you'll have a decent room, comfortable bed and not have to drag your luggage across the city for the train journey on the 26th. Book sharpish as rooms at that rate are limited.
You may search train times and fares and book your rail ticket
here; just choose to collect your ticket at a FastTicket machine at Euston.