1920 UK London House - How should I internal insulate?
That 9cm of material will be a form of plaster. However, I highly suggest you get an asbestos sample taken of it and sent away for testing. Some of these old plasters did contain asbestos previously but not all of them. You can do this fairly cheaply. Do not underestimate the danger of asbestos if you know nothing about it. Research it please. Any damage to asbestos containing material should be sprayed with water to stop particles forming in the air and do not use a vacuum cleaner as it will spread them around. You shouldn't touch it period if it has asbestos in it as it is a notifiable substance.
If you are tight for space in the rooms then yes remove the plaster and frame the wall out with stud work and put PIR/PUR insulation boards in and leave a small cavity gap at the back of the boards. If you aren't tight for room or you find asbestos, frame directly on top of the plaster. Again installing PIR/PUR boards. In an ideal scenario you would want the insulation boards to be 100mm thick but you can get insulation boards in varying thickness. Its all about how much space you want to sacrifice for insulation gains.