How should we insulate our house in a conservation area?

We are renovating and extending our 1930s home, which has stone quoins on all of the corners and pebbledash in between. As we live in a conservation area, we only have planning permission for installing 40mm-deep external insulation boards and 10mm render between the quoins on the walls instead of the pebbledash, but this will not provide enough insulation to meet our goals.

I considered adding Kingspan stuck to plasterboard on every wall inside the house, but this would involve moving a staircase and destroying wood panelling in two rooms, so won’t be possible. So would it be better to just externally insulate the property and fill in the existing empty cavity with insulation? Or should I scrap cavity fill completely and internally insulate all possible rooms and leave a couple of them cold?

It’s difficult to draw conclusions without understanding the site, design and its context. Personally, I am a fan of adding cavity wall insulation, but only in areas of low exposure and obviously using reputable companies. If you have pebbledash on a 1930s building then this is likely to be pretty hard and the walls should be quite rain/shower proof as a result. I would probably be inclined to add any additional insulation where I could on the inside face of the external walls, although this is of course quite disruptive as you suggest.

Installing a mechanical heat recovery and ventilation system in your new thermal envelope will also help in controlling condensation risks, including interstitial condensation. is way the external proportions of the house should stay intact.