For most houses in Grove, yes, and the council is one of the easier hurdles. Heritage protection covers a handful of buildings, and none of them is in the top grades. Grove has one conservation area. The neighbours are applying to extend their own houses all the time. The real constraint is clay under the foundations.
Grove has 23 listed buildings. All 23 are Grade II, and there are none at Grade I or Grade II*. Listing protects the whole building, inside as well as out. Changing one needs listed building consent on top of any planning permission, and that covers alterations as small as new windows or the removal of an internal wall. If you are buying one of those 23, Historic England's listing will matter more to your plans than the size of your budget. For everyone else, listing never comes into it.
There is a single conservation area, named Grove after the village and covering its older core. Inside a conservation area the council takes a closer interest in how a building looks from the street. Some works that would need no application elsewhere may need one, and demolition and work to trees come under extra control. Look up whether the house sits inside the boundary on the Vale of White Horse council's conservation area map. It decides which set of rules you are working under.
The Vale of White Horse council logged 149 planning applications in Grove between April 2024 and June 2026, and 78 of them in the most recent twelve months. That means 78 households in a single year looked at the house they had bought and decided it needed more room. Half of Grove's homes have three bedrooms, so a great many of those applications are a family adding a fourth.
The ground matters more than the rules. The British Geological Survey's highest shrink-swell class for clay in Grove is class 3, and about 43% of the area reaches that class or above. Shrink-swell clay grows when it is wet and shrinks when it dries. Foundations for an extension may need to go deeper than a builder would usually dig, especially near trees. Get a structural engineer to look at the ground first. It is a cost to plan for, and no reason to panic.
The village is mostly post-war houses outside the conservation area and away from the listed buildings. For those homes, many rear extensions, loft conversions and outbuildings fall under permitted development rights, which allow certain work without a planning application, within size limits. Anything bigger goes through an ordinary planning application. The 23 listed buildings and the homes inside the conservation area are the main exceptions, and the council will want an application for a wider range of work on those.
Your freedom to extend in Grove is middling. Planning is relaxed for most homes, and the clay underneath is the thing to budget for.