Has no one had experience or has no one replied?
Anyway ... I've taken my WIndcheetah on a few trains and the experience has been variable but mainly good (in the case of the old Virgin rolling stock with a guards van - the experience was fabulous: leaving London on a Friday evening I had a ticket and a reservation for the trike but not for a seat so the train conductor suggested I sit in First, where there were free seats, as it was nearer to the bike storage. I think he must have been a cyclist - knowing that you like to stay close to your steed)
Newer Virgin trains on the West Coast line (Pendolinos) have bike storage which will take a trike although, if there's another bike or already piles of luggage (which shouldn't be there), it's tricky. Staff have always been helpful and reminded me to let the train manager know there's a bike to unload at my stop (as you have to get a member of staff to open the access door from the outside - good security)
The smaller commuter trains used by First NorthWestern and Scotrail are pretty hopeless - the bike storage areas double as luggage/disabled areas in the middle of the trains so your chance of getting a trike in is low unless it's an empty train. Even if you have a booking/reservation, a disabled person without a reservation will take precedence (what do they do if there's more than one wheelchair?) but again staff have usually been obliging (one case in Scotland of a real miseryguts of a conductor was, I feel, an exception).
So overall, probably do-able but I'd find out what sort of bike storage the trains you intend to use have. The old guard's vans are so rare now they're hardly worth mentioning.