cavity wall insulation and the heatwave

[bargepole]

Just wondered if cavity wall insulation causes properties to be warmer or cooler in this hot weather?

[wildwood]

The purpose of insulation is to retard the temperature transfer from one side of the wall to the other, so if your house is cool it should slow down the permeation of outside heat in warmer weather. In the winter it serves to keep the house warmer by preventing the cold form coming through the walls.
Unfortunately, if you don't have double glazing most of the heat transfer occurs through the glass, so to keep the house cool in the hot weather it would help to keep the drapes drawn while you go to work. Again, the curtains would act like an insulator by slowing down the air movement between the glass and the house.