The way I found the times, a couple of years back, was to look at The British Pullman website, where dates and destinations are given, together with principle timings.
For the steam hauled dates, I used uksteam.info to get the detailed and up-to-date timings and routes. I don't know whether similar data is available for the non-steam trips but I'm sure that a bit of googling will turn up some useful information for you.
Good luck and happy hunting!