Looking through my pages, the C12 does seem the most likely.
Note the front axle is not a driver - so considernig the length, this is probably a 4-6-2T, 2-6-4T, or 4-4-2T. C12 was a GNR Ivatt which makes sense for Kings Cross. The dome also has an Ivatt feel about it.
Of course, it might not be entirely accurate - it could be fictional or a hybrid. Even Turner (one of the best-known painters of ships and seascapes) managed to re-arrange the mast and chimney on the tug in The Fighting Temeraire!
As for the book: No spoilers please! I'm still reading it. Yes it is a short book, but I've been busy recently
For the films, I've only seen the Hitchcock version. In that version, Hannay does indeed flee to Scotland on the Flying Scotsman (train) via Kings Cross. This is the famous 'goof' where the train starts off correctly hauled by an A1/A3, but is seen departing a tunnel hauled by something of GWR construction!
Interestingly, the book has Hannay fleeing from London via St Pancras and the Midland Railway! I guess the publisher must have been thinking of the film(s) when choosing the cover picture.
Richard