Well we went to the dental clinic, then to radiology at the hospital and then back to the dental clinic. Fortunately they are very close.
It turns out that Matthew has an extra tooth!
It is coming down where one of his adult front teeth at the top should be. It is conical and pointy, quite a bit narrower than the space left by his baby tooth, and is only just emerging. Both his adult teeth (front, top) are present.
But you can see from his picture than it has taken on enormous proportions in his mind.
A lesson there for me to be more careful how I talk about things.