That's the fella Rob. The long bolt had somehow sheared off, leaving just the eye part attached to the chain. I couldn't work out how it had stayed in place until I found the bolt fallen down behind!
I had another look behind the basin and realised that the stay used to have a long threaded piece on the back, with a nut to secure it in place. Somehow this had sheared off, and fallen behind the sink. So I just need to buy a new stay for a couple of quid.
Our bathroom basin's sink chain broke so I bought a new one. As I was removing the broken one from the basin, the stay (I think it's called?) attaching it to the basin came off. Seems like whatever was holding it in place has dried/perished.
So now I have a small hole and no way of fixing the...