Painting or rendering a standard house is normally exempt because it is maintenance and improvement. It is not exempt on a protected structure, and in an architectural conservation area a significant change of finish or colour can require permission.
Rendering over previously exposed brick or stone changes the appearance considerably and is the case most likely to attract attention, especially on a terrace or in a conservation area.
Technically, applying cement render or impermeable masonry paint to a solid stone or brick wall can trap moisture and cause internal dampness and decay. Older solid walls need vapour-open lime-based systems.