OK. So I can reach in and feel that the drain hole is open but the water has collected in the trough at the back and refrozen. A few defrost cycles later and it has filled the depression at the bottom of the freezer and is leaking out onto the floor.
I can clear out all the ice but in a few days it'll be on the floor.

To clarify, the drain hole IS open: when I use a hair dryer to melt the ice, it will easlily flow down the tube.