Yes, in most of Wheatley, though the old core comes with conditions. The village has nearly a hundred listed buildings. It has a conservation area of its own. The post-war streets beyond it face far fewer rules. Which side of that line your house falls on decides whether an extension is a builder's job or a long correspondence.
Historic England lists 99 buildings in and around Wheatley: 2 at Grade I, 6 at Grade II* and 91 at Grade II. Listing covers the whole building, inside and out, so changing a listed house needs listed building consent on top of any planning permission, and that applies to windows, walls and fittings as well as extensions. With 91 Grade II buildings, the odds that the old cottage you are viewing is one of them are better than you might hope. Owners of listed houses spend a lot of time in correspondence with the council about things they could once have changed in an afternoon.
There is one conservation area, and it carries the village's name. Inside it, South Oxfordshire District Council looks harder at anything visible from the street, demolition needs consent, and the usual allowances for extending without a full application are narrower. Check the boundary with the council for the exact house, because a garden wall can be the difference between a straightforward application and a long one.
Two scheduled monuments lie in the surrounding area. That is the strictest tier of protection, and it only really matters if your land runs up against one.
The neighbours are building anyway. South Oxfordshire's planning register shows 416 applications in and around Wheatley between April 2024 and June 2026, 181 of them in the latest twelve months. Not all of those will be extensions, and the count says nothing about how many were approved, but it is a village where the scaffolding is never all taken down at once. People who buy a three-bedroom house here and stay ten years tend to finish with four.
The ground needs a little thought too. Every postcode in Wheatley reaches class 3 on the British Geological Survey's shrink-swell hazard rating, a published geological classification for clay soils that swell when wet and shrink when dry. For an extension that usually means deeper foundations and a structural engineer's view on the soil and any nearby trees, since tree roots drying out clay are a common cause of movement. Dig deeper and pay for that up front, which costs far less than fixing a crack later.
In practice, a house on one of the post-war streets outside the conservation area will usually have the national permitted development rights, which allow a modest rear extension or a loft conversion without a full planning application, though the details depend on the house and its history. Inside the conservation area, those allowances shrink and more work needs an application. A listed house needs consent for nearly everything. Ask the council which category the house falls into, because the answer changes what the extension costs and how long it takes more than any architect's drawing.
Freedom to extend in Wheatley is middling: generous on the newer streets, tight in the old village, with clay underneath both. The paperwork depends on where the house is, and the foundations will be deep either way.