Yeah, it's wood subfloor. I'll follow your advice and simply see how I get on. I'm worried about cracking the tile as they were laid when we moved in, no spares, and I've no idea where they are from!
My suspicion is that the tile has debonded from the subfloor. On the main problem tile, you can see where one of the corners lifts and raises as you apply weight to it. Anyway, we'll see. If it is a case of the tile has debonded, hopefully I'll be able to prise it up without breakage.