Yes, most houses in Wooburn can be extended, as long as yours isn't listed or inside one of the two old village cores. About a dozen buildings are listed. Two conservation areas cover the historic centres. The neighbours put in plans all the time. The ground underneath has views of its own.
Wooburn has 12 listed buildings. None is Grade I, one is Grade II* and the other 11 are Grade II. Listing protects the whole building, inside and out, so most changes to a listed house need listed building consent from the council as well as any planning permission, including some that would need no permission on an ordinary house. Twelve is a small number for a village with two historic centres. Most buyers here will never deal with listing at all, and the few who do will deal with it for every window.
Two conservation areas cover Wooburn's older parts, Wooburn Green and Wooburn Town. Inside them, the council controls more than it does elsewhere: demolition, work to trees and some changes to how a house looks from the street all need its say-so. Buckinghamshire Council publishes the boundary maps, and they are worth checking for the exact house, because the line can run between two neighbouring properties. Outside those boundaries, most of the village is unlisted post-war housing with no extra heritage controls.
Planning records for the area list 814 applications between April 2024 and June 2026, 372 of them in the last twelve months. People here clearly change their homes. Some people here also watch closely: the residents' associations of Wooburn and Bourne End were lobbying to keep Slate Meadow free of housing as long ago as 1997. A rear extension in Wooburn will be read by neighbours who have been reading planning notices for decades.
The British Geological Survey puts every postcode in Wooburn in class 3 for shrink-swell, meaning clay in the ground that swells when wet and shrinks when dry. That is a published hazard class, and it matters most for foundations. Building regulations may require new footings to go deeper than on firmer ground, especially near trees. A structural engineer's view at design stage costs far less than finding out about the clay after the walls are up.
For an unlisted house outside the two conservation areas, many modest extensions can go ahead under permitted development, the national rules that allow some work without a full planning application, though size and position still matter. Inside a conservation area some of those rights are reduced, and for a listed building almost any meaningful change needs consent. In Wooburn, which of those three applies to your house matters more than what you want to build.
Your freedom to extend a house in Wooburn is middling. Most of the post-war stock gives an owner plenty of room, while the green, the old village centre and the clay underneath give everyone else something to work around.