Yes, but expect to deal with the council before the builders. There are hundreds of listed buildings in the area. Seven conservation areas surround the village. The clay under most of it moves with the weather. You can extend here, but the planning is part of the project.
The Brockham area has 242 listed buildings: 1 at Grade I, 10 at Grade II* and 231 at Grade II. If the house you're buying is one of them, most changes that affect its character need listed building consent, and that covers the inside as well as the outside. Grade II is the most common grade, and the one people tend to underestimate. A new window, a moved wall or a replaced staircase can each need permission, and unauthorised work to a listed building is a criminal offence, not just a planning dispute.
There are 7 conservation areas nearby, including Brockham itself, Betchworth, Buckland, Leigh and Walton on the Hill. In a conservation area, the council controls what changes on the outside of a house more closely, and some work that would normally go ahead without an application needs one. Before assuming you can build something without asking, confirm with the council whether the house is inside a boundary.
There are also 22 scheduled monuments in and around the area, including Betchworth Castle and Brockham Lime Works. That's the strictest level of protection, and it matters mainly if your land is close to one.
People here do alter their homes, though. There were 6,570 planning applications in the area between April 2024 and July 2026, and 2,434 of them came in the last 12 months. That's a lot of people applying for extensions, conservatories and loft conversions, and a large queue for the planning officers. Those figures say how often people apply, not how often they get permission.
The ground matters as much as the paperwork. The geological survey rates shrink-swell risk here at up to class 3 on its scale, and about 86% of the area reaches class 3 or above. Shrink-swell clay expands when wet and shrinks when dry, so foundations have to go deep enough to sit below the movement. For an extension, that usually means a structural engineer's input on foundation depth, and nearby trees make it worse. It won't stop you building, but it will affect the design and the cost.
In practice, permitted development rights, which let you do some work without applying, go only so far here. A house outside every conservation area and not listed may be able to do a modest rear extension without an application. A listed house, or one inside a conservation area, should assume every visible change needs permission. Check the house's status before you exchange, not after you've hired an architect.
Your freedom to change a house in Brockham is limited. Plenty of people get extensions approved, but only after the council and a structural engineer have had their say.