Yes, and Hamstreet puts fewer obstacles in the way than most villages its age. Only a handful of buildings are listed. None of the village sits in a conservation area. The neighbours send in planning applications at a steady rate. The main thing between you and a new kitchen is usually the builder's diary.
Historic England lists 10 buildings in and around Hamstreet, all of them Grade II, with none at Grade I or Grade II*. If you buy one of those ten, any alteration that affects its character needs listed building consent on top of any planning permission, and that covers inside as well as out. Replacing windows, knocking through a wall or moving a staircase can all need consent. Owners of a listed house learn that "original features" is a legal category, not a phrase from the listing. For everyone else in the village, those ten buildings are good to look at and nothing more.
The planning register confirms that people here do build. From April 2024 to June 2026 there were 730 planning applications across the area, and 343 of them came in the last twelve months. That is a lot of side returns, loft conversions and garden rooms for a village of this size. Before you worry about whether an extension is allowed, it's worth noticing how many of your future neighbours have already done one.
In practice, most unlisted houses outside a conservation area can use the national permitted development rights for modest rear extensions, loft conversions and outbuildings without a full planning application. Those rights come with size and position limits, and some estates have had them removed by condition, so check the title and the property's planning history before assuming. Anything larger or closer to the boundary goes through a normal application. That process is usually more about the neighbours' patience than a heritage officer's opinion.
Your freedom to extend or alter a home is one of Hamstreet's strengths. The rules exist, but few properties are caught by them, and for most houses the permission is less of an obstacle than the budget.