I’ve repaired the Dyson with the awesome power of @sugru and a metal bolt
Update: As I had a few people ask me what the problem was: on top of the cyclone chamber there’s a pair of washable filters in a compartment. You can open this by pressing a catch on top, however the plastic lugs that formed part of the hinge on the back cracked. As these are structural and allow you to lift the whole cyclone chamber out for emptying it was a bit of a pain. A bit of sugru and a screw later I have one replacement hinge.