I am not an expert on the area and the following may not have been the quickest way from Nottingham to York but if you want authentic travel times and mileages you could travel Nottingham (Midland) to Derby (Midland) and change there for York.
Visit the site
www.timetableworld.com and you will find the cover of the London Midland Scottish Railway tt for June 1947. Click on the cover and consult table 208 which also has some mileages. I think a route map is included in the tt. Good luck