Yes, but plan on asking permission more often than you'd like. Hundreds of listed buildings dot the area. The neighbours file planning applications by the thousand. Almost the whole town sits on clay that swells and shrinks. Extending here is common. Extending quickly is not.
Historic England's list records 347 listed buildings in the area: three at grade I, 13 at grade II* and 331 at grade II. Listing covers the whole building, inside and out, and any change that affects its character needs listed building consent on top of any planning permission. That can include things most owners would think of as maintenance: windows, doors, internal walls, even the render. Doing the work first and asking afterwards is a criminal offence, not a paperwork slip. For a grade II house that usually means careful, like-for-like work. For the grade II* and grade I buildings, expect every drawing to be checked twice.
The mapped area contains one conservation area. Inside it, the council controls demolition and can take a closer view of anything visible from the street, and some permitted development rights for extensions and cladding are narrower than elsewhere. A council can also remove further rights with an Article 4 direction, so check whether one applies to your street before assuming anything.
There are two scheduled monuments in the area, the strictest tier of heritage protection. They matter mainly if your land sits next to one, where any groundwork can need separate consent.
People do extend here, in large numbers. The council received 5,059 planning applications between April 2024 and June 2026, and 2,136 of them came in the twelve months to June 2026. Those totals take in everything from loft dormers to replacement houses, and they say nothing about how many were approved. They do show that altering a Sevenoaks home is a queue, not a fantasy. And every one of those neighbours is also reading the notices on the lampposts, so your plans will get read too.
The ground needs its own look. The British Geological Survey places the area in class 3 for shrink-swell, and about 99% of postcodes reach that class. That's the published hazard class for clay soils that expand when wet and shrink when dry, which in practice means deeper foundations for an extension, a structural engineer's input before the builder starts, and care over large trees near the new walls. It rarely stops a project, but it can add to the foundation bill.
In practice, an ordinary detached or semi-detached house outside the conservation area and off the listed register can often use permitted development rights for a modest rear extension or loft conversion, subject to national limits and a prior-approval step for some larger rear extensions. For a listed building, a property inside the conservation area, or land in the Kent Downs Area of Outstanding Natural Beauty around the edges of town, assume you need consent and plan for the extra months. Before paying for drawings, ask the council for a lawful development certificate or a pre-application view.
Freedom to extend is limited here. You can do it, but expect a long queue and a lot of paperwork before the builders arrive.