Thanks for all those replies, they've given me plenty of good ideas to think about. I think I will start off by using my multitool to make the holes where the plasterboard fixings were much bigger so I can see what is behind the plasterboard in general and behind the holes in particular.

I'll then look at trying to fit a couple of resin fixings into the wall behind the plasterboard - I'll either attach the cupboard to them directly or use them to secure a batten to which I'll attach the cupboard.