You can, but on the council's terms, not yours. There are hundreds of listed buildings. There are twenty conservation areas. Ancient monuments are scattered through the fields. The extension is possible. Whether you get the one you wanted is the council's decision.
Across the West Malling area there are 396 listed buildings. Of those, 15 are Grade I, the top tier, 25 are Grade II*, and 356 are Grade II. Listing covers the whole building, inside and out, not just the pretty front. Changing a staircase, taking out a wall, replacing windows or building on the back of a listed house all need listed building consent on top of any planning permission, and doing the work without consent is a criminal offence, not a paperwork issue. If the house you're viewing is one of the 396, the listing is the first document to read, before the survey.
There are 20 conservation areas in and around the area, including West Malling itself, East Malling Village, Offham, Ryarsh Village and Mereworth's The Street. In a conservation area, the council cares about how a street looks as a whole, so work that would be routine elsewhere, such as changes to a roof, cladding or anything visible from the road, gets more scrutiny. Trees are protected too, so the one blocking the light in your garden may need permission before it can come down.
There are also 11 scheduled monuments in the area, the strictest tier of protection, covering sites such as St Mary's Abbey and the castle keep. They matter mainly if your land borders one. If it does, digging for foundations gets complicated quickly.
None of that has stopped people applying. The planning register shows 809 applications between April 2024 and June 2026, with 357 of them in the last twelve months. Rear extensions, loft conversions, new windows and garden rooms get applied for all the time here. Applying is the easy part. Waiting for a decision is the slow part.
In practice, where you buy matters as much as what you buy. A modern house in Kings Hill or on a newer estate outside the conservation areas can usually use permitted development rights for a modest rear extension or loft conversion without a full application, although there are still limits on size and height. A listed house, or one inside a conservation area, can lose some or all of those rights, and anything beyond like-for-like repairs usually needs consent. Before you exchange contracts, ask the council whether the house is listed, whether it sits in a conservation area and whether its permitted development rights have been removed. Get those answers before you pay for an architect.
Freedom to alter a home is the weakest thing about West Malling. The history people buy the town for is the same thing that limits what they can do to their house once they own it.