Thanks for your reply MrsTawdry.
On the X-ray it showed that the roots of the baby teeth are all still there and not showing any sign of dissolving. He has his four front adult teeth, and adult back molars, but it's the three in-between on each side, top and bottom, that are unerrupted.
I'll ask the orthodontist more questions when we see her; she's going to do a full scan of his teeth. If the extraction of the baby teeth doesn't trigger the adult teeth to come in, they will need to 'expose' the adult teeth and pull them through using the kind of brace shown in the article you linked to (thanks for that, btw). It sounds pretty unpleasant to be doing that to twelve teeth at once... But I know there could be issues of jaw development if he doesn't get his adult teeth in soon, so it's probably worth the discomfort.
The other thing I'm worrying about now is that I read that lack of growth hormone can delay adult teeth coming through, and when I measured my son I realised that he's dropped from the 60th percentile for height, where's he's always been, to about the 45th in the course of the last year. That is, he's not grown for about 12 months. So I've made a GP appointment just in case there is a link between that and his teeth not developing properly.
It's all quite worrying and it's difficult to know where to get information. A private consultation might be a good idea too, I'll see what the orthodontist has to say and then have a think.
Thanks again for your advice!