I don't know if it would help but if you can find out details of Exercise Lionheart you might be able to see how various units/vehicles were, and would have been, transported. This was a large scale mobilisation exercise to test how troops and equipment, including TA, would be transported to continental Europe, should the balloon go up. I am not sure how much rail transport was used in reality.
We drove our rovers and 3 tonners from Leith to South Shields, including going through Newcastle under police escort and ignoring red lights, which was fun, and then went by an RFA ship to I think Belgium. Coming back was more relaxed, by North Sea Ferries, but I think a lot of the civvies were a bit confused by the number of squaddies on board. Clearing customs was also fun, including a 3 tonner of booze consisting of everyone's alcohol allowance.
You may be able to find out if rail was used for any transportation during the exercise, as a lot of the detail will now be declassified.