Daytime travel from London to Inverness was not possible until about 1961, when a new fast 8am train from Kings Cross to Edinburgh gave connections through to Inverness. A railway journalist of the era made an initial journey on it.
The normal previous way was overnight, which all from the Far North were used to. The principal route was from London Euston, via the Motherwell-Stirling direct line, and Perth, LMS all the way, on which there were a couple of trains a day (less than before 1939). They were very substantial and overcrowded. Most seats were taken by older passengers and women; soldiers would expect to "stand", alias lay in the corridor, even the officers in first class. In addition, there was a special daily military-only (so not suitable for your story) train from Euston right through to Thurso, which took the best part of 24 hours, although few were travelling all the way.
Tickets for a mainstream journey, London Euston to Inverness, would be the small preprinted card type, linked above, commonly called "Edmondson tickets", if you want to do a further search, after the inventor of the printing process involved. Less common trips, say Wembley to Dingwall, would be completed by hand on a paper form. There is, believe it or not, a subculture of enthusiasts about tickets, who even offer a service to those in the media, see :
http://www.transport-ticket.org.uk/contact-us/
My father told me that although there were various restricted areas around the country, which people pretty much stuck to, there was little checking, and even if a policeman stopped you, once they established that you didn't seem like a spy, they normally just gave advice, and you were on your way. It was different if, like many men, you were in uniform and stopped by the Military Police, but again there were many such men, and not a lot of MPs.
in my experience artistic license wins out over facts on TV shows!
It depends. For TV shows which are filmed on one of the historic railways, such as the Bluebell in Sussex, those from there are commonly brilliant in getting all the details right, the right uniform brass buttons, etc, so us lot won't have any complaint - though they say whether the Director accepts their suggestions is a different matter.