I spoke to a friend's sister who is a breeder. She was adamant that it was a partial shed that had cut off his circulation. On her advice I soaked him for 40 minutes on Monday and 40 minutes again this morning to see if he would shed, to no result.
I took him to the vet this afternoon. Turns out it's very definitely broken as I suspected. Apparently this is quite common in corn snakes. They're going to have to amputate that piece of the tail on Thursday. He doesn't seem to be in any pain, but they gave him a painkiller anyway.
Has anyone else had a snake have a tail amputation? What should I expect in terms of recovery?
(In case anyone's interested, the consultation plus painkiller today cost £77 and the amputation is going to cost £200-300.)