OK, lets get it right about cavity walls etc.
An open cavity wall, (one without insulation in) doesn't really work that well, as there are convection currents in an open cavity wall,so that although dry air is an almost perfect insulator, the open void really isn't as good as it should be, so that's why the powers that be invented foam infill, in it's various incarnations, none of them very effective. Often people who had their cavities filled found damp patches appearing inside due to the mortar droppings on the wall ties. ( this had been evaporated previously by the convection currents)
If you use a single skin of 4" bricks or blocks and then use 2x2" timber inside with a plaster board finish with fibreglass in the cavity, that will work as well as any other method, but choose whichever you will.
An open cavity wall, (one without insulation in) doesn't really work that well, as there are convection currents in an open cavity wall,so that although dry air is an almost perfect insulator, the open void really isn't as good as it should be, so that's why the powers that be invented foam infill, in it's various incarnations, none of them very effective. Often people who had their cavities filled found damp patches appearing inside due to the mortar droppings on the wall ties. ( this had been evaporated previously by the convection currents)
If you use a single skin of 4" bricks or blocks and then use 2x2" timber inside with a plaster board finish with fibreglass in the cavity, that will work as well as any other method, but choose whichever you will.