External solid wall insulation won’t affect the size of your rooms (unlike internal solid wall insulation) but you might need planning permission as it could change the appearance of the building. There is a wide range of colours and finishes that can be applied and all the options should be discussed with your chosen contractor. Often the existing finish can be replicated to preserve much of the original appearance of the house.
As solid wall insulation is now constituted as an ‘improvement’ rather than an ‘enlargement’ you are unlikely to need planning permission. Consent and planning permission are likely to be required if your house is listed or is located in a National Park, area of outstanding natural beauty, conservation area or within a World Heritage Site.