Peter, you are correct.
Judging by the head plumage (or lack of) in shots 1, 2 and 4 I would say that this bird is quite seriously ill. It is very common for gulls to pick up nasty diseases (avian botulism is the worst) from feeding on rotting waste at landfill sites.
I had originally put it down to the age of the birds but I have looked over the photo shoot again, including unposted images, that particular bird had difficulty in flying whilst the other did not. It looks as though you are correct in your post. What a shame that such a young bird is afflicted. I hope it recovers but I shall never know.
Nice photos. Yes, not sure how common it would be to be missing all his head feathers at this age.