External wall insulation to a house is usually treated as improvement work that does not need permission where it does not materially alter the external appearance so as to render it inconsistent with the character of the structure or neighbouring buildings — but a protected structure or an architectural conservation area changes that.
For a standard house, wrapping the external walls and re-rendering typically reads as maintenance and improvement rather than development requiring permission, provided the finished appearance remains consistent with the character of the house and the street.
The position is different for a protected structure, where works affecting the character of the structure need permission, and in an architectural conservation area, where external changes are more tightly controlled. Removing original render, mouldings or exposing brickwork detail can also tip an ordinary house into needing permission.