Yes, and more easily than in most towns this old. There are only a handful of listed buildings. No conservation area falls within the town's mapped area. Neighbours file planning applications all the time. Unless you own one of the few protected buildings, the main thing standing between you and a rear extension is a builder who answers the phone.
Heathfield has 13 listed buildings: none at Grade I, 1 at Grade II* and 12 at Grade II. Listing covers the whole building, inside and out, so owners need listed building consent for most changes that affect its character, down to windows, fireplaces and internal walls, and carrying out work without consent is a criminal offence, not a planning misunderstanding. The listing will be in the sale particulars, or it should be. In a town of this size, 13 listed buildings is a short list, and the odds that you have bought one of them by accident are low.
What the neighbours do settles the question. Between April 2024 and June 2026, 747 planning applications were lodged in the area, 325 of them in the last twelve months. That is a steady flow of people extending, converting and adjusting homes, and the planning office sees plenty of new rear windows and loft extensions. Anyone who tells you Heathfield is a hard place to build has not read the list of applications.
One listed building in the area is on Historic England's Heritage at Risk register. That is a label for a building in poor condition, which attracts scrutiny of any work and can sometimes attract grant support for repairs. It is a problem for whoever owns that building, not a hazard for the buyer of an ordinary semi down the road.
In practice, most homes here are ordinary post-war houses and bungalows with no listing, so many single-storey rear extensions, loft conversions and outbuildings can go ahead as permitted development, the national rights that allow certain work without a full planning application, provided the house keeps those rights and the work stays within the size limits. Check that previous owners or a planning condition have not removed them. A small part of the area falls within the High Weald Area of Outstanding Natural Beauty, where some permitted development rights are narrower, so confirm which side of that line the house sits on. Anything bigger than the standard limits goes through ordinary planning, and anything touching a listed building needs its own consent.
Freedom to extend is one of Heathfield's real strengths. The protected buildings are few, and for everything else the process is routine paperwork, not a battle with heritage officers.