I actually have a casement AC window unit. Not sure if this is the same dimensions as a UK casement window. It is as if you took a window AC unit and made it vertical orientation. My window still slides up and blocks the remaining void, but I imagine it would work just fine if it swung out and you built a plexiglass or plywood cover. Maybe you can also unscrew the swinging window and put it away in a closet.
The AC unit is a little different than "traditional" window units. There is no slot or anything really to grab on to the window or the sill. It is mainly secured by a brace that is also not screwed into anything really, just directing the weight of the external portion of the unit into the side of the exterior wall.