Often yes, but in the old town the building gets more say than the owner does. Nearly two hundred buildings are listed. The historic centre is a conservation area. The clay underneath moves with the weather. The neighbours keep applying for changes anyway, which tells you it can be done.
Petworth has 188 listed buildings. Two are Grade I, 13 are Grade II* and 173 are Grade II. Listing covers the whole building, inside and out, not just the front, and any work that affects its character needs listed building consent on top of any planning permission. Grade II is the most common grade and the least strict, but that's a comparison between strict levels. Work done without consent is a criminal matter, not a planning dispute. When a listing says "scope to extend" on a listed house here, read it as the seller's hope rather than anything the council has agreed.
The area has one conservation area, covering Petworth itself. Conservation-area status generally tightens what you can do without applying. Demolition, some roof changes and alterations facing the street are the usual pinch points, and the council judges them by what the street looks like, not by what your kitchen needs. Whether any extra local restrictions apply on top of that is something to check with the council for the specific address.
People here do alter their homes, and in numbers. There were 532 planning applications in the area between April 2024 and June 2026, and 225 in the last twelve months of that period. That's a busy planning register for a small town. It shows that owners are applying for plenty, even if the council files hold the answers.
The ground needs as much attention as the paperwork. The British Geological Survey places Petworth's shrink-swell risk at class 3, and that class covers 100% of the area. Shrink-swell means clay that expands when wet and shrinks when dry, which can move shallow foundations over time. For an extension, it means foundations may need to go deeper than a builder's standard quote assumes, and trees near the new walls need thinking about. Get a structural engineer involved before the architect's drawings are finished, not after the first crack appears. It's a factor to cost into the budget, not a reason to walk away.
In practice, a post-war semi outside the conservation area may manage a modest rear extension under permitted development, the national rights that allow some work without a planning application. A listed house anywhere, or a home in the conservation area, should assume that every change needs a conversation with the council first. Check the listing entry, check the conservation-area map and talk to the planning department before you make an offer that relies on adding a room. Those rules have long outlasted every previous owner's plans.
Your freedom to extend here is middling: easy enough on newer homes, closely controlled in the listed and historic core, and on clay that requires an engineer to sign off every foundation.