Hi and welcome to the forum Ray. The Fellsman runs every wednesday through Blackburn to Carlisle, and returns in the evening, so there are two chances for you to photograph it. Timings can be found here:
http://www.uksteam.info/tours/index.htm
If you are in the Whitby area, I would suggest you visit the North Yorkshire Moors Railway.
They also have an extensive website that you should find interesting.
Regards Mike.