Just posting to agree with what Phil has said. You may need to put a piece of wood across the general area so you can fix a screw at the right point.
A lot does depend on what sort of stone wall you have, which is presumably hidden by plaster. If it really is 'rubble filled' you will have two fair faces of squared off blocks, but there is every variant from nice square hard stone through to the sort of construction that is little more than a heap of rubble with some of the voids filled with soft lime mortar.
I've had some success just by using progressively bigger screws and fixings - going up to say 8 x 100 mm screws into matching plastic plugs where you might have expected to use 5 x 40 mm.
The old solution that is no longer available was a mixture from Rawlplug which you mixed up with water and pushed into the hole, but as it was cement and asbestos, it's no longer available.
However, there are more modern solutions where you drill a hole and inject resin to glue a bit of studding into the hole. I've not used these but a quick look at the instructions shows that the makers only recommend them for neat round holes - I suspect you could be left with a resin ended stud twiddling round in a big hole which would be no better.
However, I have seen adverts for a new solution that might be what you need. It is a disc of felt, about 50 or 75 mm diameter, which you wet, then scrunch up and poke into the hole. It holds the screw and sets solid.
The trouble is, I've not registered what it was called! I can't spot it from a quick look online at B&Q and Screwfix and Toolstation - but maybe someone else will know what they are!