Depending on the shape of your existing bungalow and the proposed overall shape you may be able to improve your form factor. The lower the form factor the easier it will be to achieve energy efficiency. Unfortunately bungalows do suffer from poor form factor.
The energy ideal for an extension is that is more thermally efficient than the wall it replaces, so that your energy usage goes down with the bigger floor area and not up. The likelihood of that happening is low, but it is a target. Build the extension to as near to Passivhaus standard as you can. You can still use traditional materials to achieve that but with great care.
Lime can be applied outside as a render or inside as plaster (or in a damp kitchen or bathroom, as an internal render) there is an insulated version containing cork granules and called Diathonite. Diathonite is a certified Passivhaus component. As Diathonite is pre coloured you can omit the wall decoration stage. Fresh plaster or render shouldn’t be decorated for a while anyway. If insulating the outsides of the walls remember to fit soffit boards after insulating and not before, allowing the insulation to reach your roof insulation.