Yes, though almost nobody here does it quietly. The town carries more than two hundred listed buildings. A conservation area sits over the historic core. Hundreds of applications have gone in over the past couple of years, so people clearly do get work done. The question is not whether a house here can be extended. It is how much of the project you are prepared to negotiate with somebody else.
Start with the listings, because they are the constraint that catches buyers out. There are 217 listed buildings in the area: 5 at grade one, 5 more at grade two star, and 207 at grade two. Listing is not a plaque on the front. It protects the whole building, inside as well as out, and works affecting its character need listed building consent on top of any planning permission. That covers the things owners assume are theirs to decide, including windows, internal walls and roof coverings. Buying period charm and then applying to remove it is a conversation that has been had here many times, and it does not usually end the way the new owner planned.
One conservation area covers the town. Conservation area status brings its own controls over demolition and external alterations, and it is the usual mechanism by which rights that would otherwise be permitted development get curtailed. Whether a specific restriction applies to a specific street is a question for the council rather than for an estate agent's particulars, and it is worth asking before the offer, not after.
There is also 1 scheduled monument in the area. That is the strictest protection tier in the system, and it matters mainly for anyone whose land sits near it, where consent sits with the national heritage body rather than the council.
None of this means nothing gets built. Between April 2024 and July 2026 there were 404 planning applications across the area, 147 of them in the last twelve months. That is a steady flow of people altering, extending and converting homes in a small coastal town, which tells you the process is navigable by ordinary owners with ordinary budgets and reasonable patience.
The ground is the other thing to price in. The British Geological Survey classifies shrink-swell hazard here at class three at its maximum, and about 88% of the area reaches that class. Shrink-swell ground moves with moisture, which is a foundation question rather than a scare story: deeper foundations, an engineer's view before the drawings are finalised, and a builder who has worked on this sort of ground before. It adds cost and time to a rear extension. It does not stop one.
The practical shape of it is this. In the historic core, assume you need consent for anything visible and quite a lot that is not. Away from the protected streets, ordinary permitted development rules do more of the work, and a modest rear extension becomes a normal job with a geology problem attached. The determining question is not what the town allows in general. It is which of those two worlds the individual address sits in, and that is answerable in an afternoon before you commit.
Freedom to alter a home here is one of the weaker parts of the offer, and it is weak for the same reason the town is desirable. The rules exist to keep it looking like the place you fell for from the harbour wall.