Cheap Virgin Train Tickets
Have a look on the Virgin Trains website. There are National Express Buses which are cheaper which you get from Victoria coach station but they take an age to get there. If you book with Virgin Trains, you can get greatly reduced prices using their Virgin Value tickets. 50 single, booking around three weeks or more in advance. From there, you will need to make your way into central London by train. Youll need to get to Victoria and then get a tube to Kings Cross.
Trains to Edinburgh go from here.
This is not exact as Ive only ever flown to Scotland before.
The website you need to go on to look at tickets is either the Virgin Trains or GNER website. Just type these into Google. It is often cheaper to book 2 single tickets instead of a return. If you book far in advance, youll get a better price.
The budget airline Easyjet fly from London to Edinburgh, you could look at prices for that too. The flight is around 45 minutes, so its a lot quicker. The weather in Edinburgh in December will probably be pretty cold and wet, as itll be winter.