Useful replies everyone, thanks.
Kim, it's next to the loo, so if I wanted to I could go for that sub-standard train travel experience in the comfort of my own home.
Cudzo, I'm not sure how hanging it upright will detract from the prettiness. It currently lives in the hall, so gets in the way a bit. Rumours that it shares a bed with me are completely unfounded.
Robgul, good shout about putting it in diagonally. However a quick trial shows the handlebars protrude if I go right into the corner. Putting a hook in the corner and slightly angled by mounting it on a suitable fillet of wood might work. However, that's really useful to hear about spreading the load with cavity fixings and a piece of ply. There's another cupboard the other side of one of the eggbox pieces, so I could put a load spreading plate in thart cupboard too, and bolt/screw all the way through. That may be the way forward.
phantasmagoriana, which hooks are those?