Usually yes, though how much depends on which part of the village the house is in. The old centre is full of listed buildings inside a conservation area, where even small changes need permission. Outside it are plenty of late-twentieth-century houses where an extension is a routine project. The neighbours keep the planning office busy, so people clearly do get work done here. The clay under the village matters as much as the planners do.
Bampton has 94 listed buildings. One is Grade I, three are Grade II* and the other 90 are Grade II. Listing protects the whole building, inside and out, so changes that would be routine elsewhere, such as new windows, a removed wall or a different roof covering, need listed building consent from the council on top of any planning permission. Starting work without that consent is a criminal offence, and the cost of putting it right falls on whoever owns the house at the time, including a buyer who inherited the problem. The higher the grade, the closer the scrutiny. In a village that was a market town by the time of the Domesday Book, many of these protected walls have been standing for centuries.
The village has one conservation area, covering the historic core of Bampton. Inside it, the council takes a closer interest in anything visible from the street, including extensions, demolition, front boundaries and some tree work, and some changes that are allowed without permission elsewhere need an application here. A rear extension on a 1990s close on the edge of the village and the same extension behind a house in the old centre can be very different jobs, even though the houses are a few minutes' walk apart.
People here do alter their homes, and often. The planning records for the area show 902 applications between April 2024 and June 2026, and 375 of them came in the last twelve months. That shows plenty of owners are trying to make changes, but it says nothing about how many get approved. A count of applications cannot tell you that.
The British Geological Survey puts Bampton in shrink-swell class 3, and 100% of postcodes in the area reach that class. Clay soils like these swell when wet and shrink in dry summers, and the movement can crack a building whose foundations are too shallow. For an extension, that usually means deeper foundations than a standard design would assume, and possibly a different foundation design near trees. Ask a structural engineer early, before the architect draws anything. The ground can affect the budget more than the drawings.
In practice, a house outside the conservation area and not listed can often use permitted development rights for modest rear extensions, loft work and outbuildings, within the national limits. A listed house, or one inside the conservation area, should be treated as needing an application for most changes. Check the council's listing and conservation-area maps for the exact house, because the boundary decides which set of rules applies.
Your freedom to extend in Bampton is middling. A newer house on the edge of the village gives you plenty of room to build, while a period house in the centre needs patient negotiation with the council and a builder who knows how to deal with the clay.