Two exterior walls in my kitchen were originally part of an outhouse and are only one brick thick. How can I upgrade and insulate these walls and address the damp problem without rebuilding?
personly, i would use 12.5mm insulation backed plasterboard secured to the walsl using dot and dab, most buildiers/carpenters will do it so if you have a reccomended one use them, its not easy to dot and dab correctly (i say correctly as anyone can stick to a wall out of square)
or, fix 2*2 timbers to the wall, fill between with fiberglass/celotex insulation and then plasterboard with 12.5mm plasterboard (put another layer over this one if you want to go belt and braces and have a very strong wall)
Try Fermacell rather than plasterbard as its load bearing and pretty immune to damp.
Remember to use a breathable damp proof membrane behind the insulation (sometimes this is built into the insulation boards) as you want to avoid condensation inside the dry walling.