Yes. Carterton is one of the easier places in this part of Oxfordshire to extend a house. No conservation area covers the town. Listed buildings are rare, and almost none are of the grand sort. The neighbours file planning applications at a steady rate. The ground is where an extension most often runs into trouble, because the clay moves.
Historic England lists 34 buildings in and around Carterton. None is Grade I, one is Grade II* and the other 33 are Grade II. Listing covers the inside of a building as well as the outside, so on any of those 34 even a new doorway or a replacement window needs listed building consent. The rest of the town's housing has no such protection. Shilton, the village this page also covers, is different: it is a conservation area, so changes to the outside of a house there get closer scrutiny than they would in town. Carterton has form for this kind of reuse: one of the wartime Robin hangars on Alvescot Road ended up as part of a motor repair garage.
Local planning records show 902 applications in the area between April 2024 and June 2026, and 375 in the twelve months to June 2026. That is a steady flow of people changing their houses. Applications cover everything from a porch to a new house, and the records do not reliably say how many were approved, so the count tells you about activity and nothing about your chances.
The ground matters more here than the planning office does. The British Geological Survey's hazard mapping puts shrink-swell clay in Carterton at class 3, and about 63% of the area reaches that class or above. Clay at that level swells when wet and shrinks when dry, and foundations have to go deep enough to sit below that movement. Get a structural engineer involved before you finalise any design. Deeper foundations or a trench-fill specification can add real cost to the build, and they cost far more to put right later. The trees in the back garden also count, because their roots draw moisture out of the clay.
For most houses in Carterton, the planning question comes down to permitted development: the national rules that let ordinary houses take smaller rear extensions, loft conversions and outbuildings without a full application, within size limits. Those rights do not apply to flats or listed buildings, and they apply more tightly in conservation areas such as Shilton. Much of Carterton was built in large planned phases, and those approvals sometimes came with conditions that removed or restricted permitted development rights. Ask West Oxfordshire District Council whether the permissions for the house you are buying limited them, since that can turn a straightforward extension into a full planning application.
Freedom to extend is one of Carterton's real strengths. The planners will rarely stand in the way, so the extra cost and effort usually goes on the foundations.