How long will the journey be, in total? I know crewe to glasgow is three hours (used to do it every weekend and back!), so I'm guessing at least double that. TBH I think it would be a struggle in a car, never mind on a train!
You'll definitely need separate carriers for all of them, as even in a large carrier two will be cramped. You'll need a way to offer them water (which might be difficult on a crowded train as you can't risk them escaping through the door, but a bowl left in the carrier would spill, and unlimited access would also mean lots of toilet breaks - possibly ice cubes kept in a small cool bag, so you could just put in one at a time, each hour or something?). Depending on the length of the journey, not feeding the cats the night before and limiting their water should suffice when it comes to toileting - they won't go in their carriers.
If you were travelling in an estate car, I would suggest a large dog crate in the boot for all three of them, with a litter tray in the corner and one of those non-spill water bowls, but this would be impossible on a normal train (some of the sleeper trains have separate cabins, in which case it would be easier as you could just book it as a whole, and some have seperate luggage carriages where they will accept large crates, but obviously you'll be changing trains).
Is hiring a car (or van) not possible? If you were taking them on the train you'd need to book extra seats to hold the carriers, so it could end up being quite costly anyway.