Command Strips are good but only for lightweight art such as canvases. I wouldn’t use them for mirrors.

It depends on the weight of what you’re looking to hang. I’ve used GripIt plasterboard fixings for TVs, self-drill plasterboard fixings for mirrors, normal rawlplugs for large pictures and pins for small pictures. This is all with insulated plasterboard. The only time we’ve used some fixings all the way through the insulation into the brick is for built in wardrobes.

Heavier things should ideally be mounted on the studs, all the way through your plasterboard. But since you don't want to randomly pierce your foil/insulation, use plugs for hollow walls for the lighter items, thus with short screws.

For bookshelves i used molly anchors, as they have a flat bolt, hoping they would push the foil instead of pierce. For artwork and pictures, a picture rail system is ideal, as the studs are along the top of the wall anyway.

Thank you for the images of the different types of screws and suggestions. They are all very useful.

Due to being an old brick wall (not cavity) we're thinking more toward the natural fiber insulation (wood or wool) rather than foil and man made materials. Realistically it'll be about 60-70mm thick and I'm not convinced plasterboard is the best method of covering, however if we go that way the plaster board fitting sound great.

I am specifically thinking about curtain rails with curtains large enough to cover victorian windows. Reasonably weighty.

It looks suspiciously like one needs to plan securing points prior to insulation if using natural (thicker) insulation products.

We used alkreflex in our home, as the footprint is 6x6m we went for the thinnest option. It required 22mm gap (wooden slats) + foil + 22mm gap (wooden slats) + plasterboard, a total of roughly 6cm. And it won't rot, it's totally waterproof and doesn't itch when applying!

They should give me money for this, it sounds like advertising.

When we insulated our walls with cellulose insulation, I was worried about the same thing—how to attach stuff like shelves and curtain rails. What worked for us was using longer screws and going through the insulation into the studs. For heavy items like mirrors or shelves, we used anchors that go deep enough to reach the structural wall. It takes a little extra planning, but it definitely works. For curtain rails, we made sure to attach them directly to the studs with longer screws.