He's got squamous cell carcinoma, which means a sodding great lump in his mouth.
We have been giving him squashy things to eat (yum yum) and regular flannel-baths (yuck).
Here he is in happier times:
Update (6 Feb). He's been getting increasingly alarming of appearance (pulling his own fur out because his tongue's not working) and thin as well. As well as that, he's hungry ALL the time. We are in the midst of making the most difficult sort of decision ...