Yes, but the paperwork gets a vote before the builder does. Over 150 buildings are listed. Four conservation areas cover the village and its hamlets. The whole place sits inside a protected landscape. You can extend a home in Box, but you can't do it quickly or quietly.
Historic England's list puts 153 listed buildings in and around Box: 1 at Grade I, 5 at Grade II* and 147 at Grade II. Listing covers the whole building, inside and out, not only the front elevation, so if your house is on that list almost any change that affects its character needs listed building consent, from an extension down to replacing old windows or knocking through an internal wall. Doing the work without consent is a criminal offence rather than a planning slap on the wrist, and the liability passes with the house. Buyers who assume the last owner sorted it all out can find themselves paying to undo someone else's kitchen.
There are 4 conservation areas: Box itself, designated in 1975 and extended in 1991, plus Ashley, Ditteridge and Middlehill, all added that same year. Inside a conservation area, the council controls demolition and looks harder at anything visible from the street, and the list of things you can do without asking gets shorter. On top of that, the whole of Box lies within the Cotswolds Area of Outstanding Natural Beauty, and the parish falls in the easternmost part of the Avon Green Belt. That's three layers of protection before anyone has looked at your drawings. The stone and the views are what you paid for, and the rules exist so the next buyer gets the same ones.
There are 2 scheduled monuments in the area, the strictest tier of protection there is. They matter mainly if your land sits next to one, where even digging foundations can become a conversation with people who are more interested in what's underneath than in your utility room.
None of this stops people trying, and the planning register proves it. Between April 2024 and June 2026 there were 461 planning applications in the area, 209 of them in the last twelve months. Box is not frozen. It's a village where people alter their homes all the time, and do it by filling in forms rather than by hiring a skip on a Friday and hoping.
In practice, assume the answer to "do I need permission?" is yes until someone qualified says otherwise. Permitted development rights, the national allowances that let you build some extensions without applying, are narrower in conservation areas and Areas of Outstanding Natural Beauty and don't apply to listed buildings in the same way at all. Before you buy, check whether the house is listed, whether it sits inside one of the four conservation areas, and what the planning history on that address shows. A pre-application conversation with Wiltshire Council costs less than a refused scheme and a redesign. The buyer who budgets for the architect and never the heritage consultant tends to meet the heritage consultant anyway, only later and at a higher price.
Freedom to extend is one of Box's weaker points: extensions happen here all the time, but only for people with patience, a good architect, and no romantic attachment to a glass box on the back of a listed cottage.