> ...use spray adhesive and then fix the plasterboard to the wall through the
> insulation with a few plastic insulation fixings like these

Those things are fine for holdinging insulation against a wall but that I about all I would use them for.
Have you discussed your insulation plans with your builder yet or are you doing this all yourself?

I don't think it is a good idea to just add a layer of insulation and a layer of board. There is a lot more detail to it than this.

For boards internally to stone walls it is more usual to put up timber studwork. Then insulate between and optionally behind and/or in front of the studwork. That way you can fairly sure the internal surface will be straight and won't move much. As Tony says, detail at door and window reveals will require a little more work too.

Someone mentioned a parge coat on the internal stone surface. It's not a bad idea. I would be reluctant to trust it 100% though. I would be worried about moisture tracking through the wall. These old stone walls can move when messed with like this and then any moisture that can track across/through the wall would emerge at the cracks. Once it's in there would be little you can do to fix it. The studwork will let you leave a small air gap between insulation and stone.

So the other thing you will need is membrane(s). Wind will probably come blasting through that stone wall so it would be a good idea to fit an outer windproof membrane of some sort between wall and studwork to stop it blowing through and around your insulation.

Inner insulation will isolate the stonework thermally. So rather than being the warm thermal mass that it is now it will be cold and the inside of the room will have almost no thermal mass (except your UFH screed presumably). Your room will warm up much more quickly this way when heated but any moisture from inside will pass through your boards and condense on the cold stone. To prevent this you also need a breathable VCL on the inside between insulation and internal boarding.

The inner membrane will also be responsibel for most of your air tightness so real attention to detail at reveals and taped joints is crucial. Many of us see these taped joints as a bit of a potential weak spot too.

Sorry, yes, it is kind of a typo. The membrane does not really need to be breathable. You just need something to keep the moisture on the warm side away from the colder layers. I just automatically typed breathable because of the products we have used here.

If you have inner and outer membranes then at least one of them needs to be breathable. The wind-stopping membrane on the outside can be breathable (like Solitex, that's what we used last time although I'm not quite convinced about the methods of joining it - it does not seem to tape well).

However there certainly are breathable VCL membrames. The earliest of these is probably Tyvek and it is still well used commercially as an outer membrane in some types of construction. More recent innovations include adaptive breathable VCL like Intello (for internal use) which change pore size with the seasons. Wikipedia and Google will turn up plenty more info about these.