Hi Big-All and thanks so much for your quick reply and friendly welcome! I think it's a concealed hinge. It goes straight into the board, and there's not another hinge on the other side of the board, so I'll try your wood glue and clamp suggestion. Once again, many thanks!
I'm ashamed to admit that I have an MDF kitchen, and recently the screws on the hinge of one of the doors have become looser and looser. I've regularly tightened them up but clearly the MDF has been gradually crumbling and just today the hinge has come out entirely. There's no use trying to...