A good while ago I bought a Delsey suitcase in which a Brompton would fit. It was very big and I don't know if it would make you push the 20Kg limit. At the time it was the only one I could find to fit the bike in. I used it to fly to Budapest & back a few times on cheapo airlines, so I suppose it was light enough.
I did fly with the Brommie in the Brompton soft case & it did incur damage to the mudguard stays, easily fixed, but I had gone to some lengths to pad it with old jumpers and stuff around the vulnerable bits. I wouldn't fly with one in such a case again, but on a train, with more control over things, maybe you'd get away with it.