Yes, and plenty of people already are. The catch is geography rather than policy: the old core carries nearly all the protection and the newer edges carry almost none. One side of a boundary line means an application, a set of drawings and a conversation about window materials. The other side means a builder and a start date. Same town, two completely different projects.
There are 216 listed buildings in and around Shepton Mallet, one at Grade I, 10 at Grade II star and 205 at Grade II. Listing covers the whole building, inside as well as out, which catches out anyone assuming it stops at the front elevation. Replacing windows, taking out an internal wall, changing a roof covering or fixing panels to a street-facing slope all turn into consent questions rather than decisions, and that consent sits alongside planning permission rather than replacing it.
One conservation area covers the town, and its boundary is the first thing worth establishing before an offer goes in. Inside it the usual permitted development freedoms narrow, external changes get judged on how they read from the street, and the route to the same extension gets longer. None of that is a refusal. It is a slower yes, with somebody else's taste applied along the way.
Three scheduled monuments sit within the area, which is the strictest tier of protection in the system. That matters if a plot runs up against one, and is otherwise a line in the search results rather than an obstacle.
People do build here, and the volume settles the question. Between April 2024 and June 2026, 677 planning applications were submitted across the area, 284 of them in the last twelve months. Whatever the constraints are doing, they are not stopping anyone from trying.
One listed building in the area appears on Historic England's Heritage at Risk register. That means a building in poor condition, where repair work can attract grant support and will certainly attract attention. For anyone buying an ordinary house nearby it is context rather than a problem, though it is a fair signal of how closely the older stock gets watched.
In practice the town offers two different planning experiences. On the newer estates and the outer edges, permitted development behaves the way it behaves anywhere, and a rear extension is a matter between you, a builder and the building regulations. In the older centre, assume consent is needed for anything visible, budget for drawings and a heritage statement, and accept that the timetable belongs to someone else entirely. Which of those two lives you get is decided by the house, not by your enthusiasm.
Freedom to alter a home is the weakest thing this town offers, and it is weakest precisely where the housing is most appealing. The frontage that made you want the place is the same frontage that will be reading your plans.