For many years now I have regularly made journeys between North London and Doncaster. Until a couple of years ago I would almost always take the train. What has changed is twofold - I moved to a more outlying part of London, and public transport up north has degenerated further. So the journey between KGX>DON is fantastically quick and efficient as ever, but when I take into account the tube journey at this end, the unreliable Firstbus at the other end, it is unfortunately now more convenient to drive.
But, going back to the purely cost element, approximate cost for a round trip is £70 in fuel based on current prices and 35mpg. That still compares favourably with an open return which must be north of £100 now.