Thanks for the advice!
We tried phoning Virgin Trains - nothing doing. National Express (ie GNER) said they would take things in the goods carriage for £5 per item if they could be carried by one person alone. The rules on this seem a bit flexible and varied depending on who we spoke to, but someone quoted boxes of no more than 1.5m by 0.5m by 0.5m.
In the end posted a free wanted advert on Gumtree liftshare section and got a couple of calls, one guy who is driving a van nearby, so we're sharing the petrol costs and getting our stuff up there.
Cheers for the flightcase tips. Didn't know of the SKB cases.