Well!
I think I have been rather lucky.
We pulled the machine out, took out the pipes etc. so we could get to the back of it (all good practice for moving it and re-installing), and had a look inside:
The belt had simply slipped off and was lounging around in the bottom!
So we popped it back on and things seem to be going pretty well now. Spin cycles and everything.
Thanks for all your advice, I probably wouldn’t have opened it up if you hadn’t been so unflinching at the suggestion 😀
Heli