Yes, and Copthorne makes it easier than most villages do. There's no conservation area drawn over the place. The listed buildings are few and all at the most common grade. Neighbours apply for planning permission constantly. The biggest obstacle to your extension is likely to live next door, not in a heritage register.
Copthorne has 14 listed buildings, and all 14 are Grade II. None are Grade I and none are Grade II*. Listing protects the whole building, inside and out, so changing a listed home, even replacing windows or moving an internal wall, needs listed building consent on top of any planning permission. It's a slower, more careful process that rewards patience and a builder who has done it before. For the vast majority of homes in the village, none of it applies, and if your house is one of the fourteen, the sale paperwork will tell you well before the builders arrive. There's also no conservation area within the village's bounds, which removes the extra layer of control over things like demolition, cladding and street-facing changes that catches out buyers elsewhere.
There's one scheduled monument in the area, the strictest tier of protection. It matters to anyone whose land sits near it and to almost nobody else.
People here clearly do alter their homes. Across the area's planning records, 2,460 applications were submitted between April 2024 and June 2026, with 1,089 of them in the last twelve months. That's the paper trail of loft conversions, rear extensions and garage rethinks. Nobody fills in planning forms that often in a place where the answer is always no.
In practice, many smaller changes to an ordinary house, such as a modest single-storey rear extension or some loft work, can go ahead under permitted development rights without a full planning application, within size and design limits. Anything larger, anything facing the street, or anything on a listed building needs consent. Previous owners may already have used up some of those rights, and some estates have conditions removing them, so the planning history of the specific house decides how much you can do. Check it before you offer, not after you've shown your partner a sketch of the kitchen. Mid Sussex District Council's planning register is where the answer lives, and a lawful development certificate is the cheap way to be sure before building work begins.
Copthorne is an easy place to add a room. Unless your house is one of the handful that are listed, the rules are the ordinary national ones, and your neighbours are testing them all the time.