Mostly yes, provided your house isn't one of the ones history has already claimed. Battle has well over a hundred listed buildings. The whole town sits inside a protected landscape. The neighbours put in planning applications all the time. Your kitchen can probably be extended. The abbey can't.
Historic England lists 141 buildings in the area: 5 at Grade I, 6 at Grade II* and 130 at Grade II. Listing covers the whole building, inside and out, so changing anything that affects its character needs listed building consent on top of any planning permission. Replacement windows, knocking through a wall and an extension on the back all count. Most of the 141 are Grade II, so if you're buying a listed house here, it's almost certainly one of those. You'll own it, but plenty of other people will have a say in what you do to it. No conservation area shows up in the heritage data used here, which leaves listing and the landscape designation as the main controls.
The area has 1 scheduled monument, the strictest tier of protection there is. It matters mainly if your land sits next to or on top of one. A garden shed on a scheduled monument is a conversation nobody wins.
The planning register shows how much people here want to change their homes. Rother recorded 750 applications for the area between March 2024 and June 2026, 297 of them in the last twelve months. That's a steady flow of people asking to alter houses in a town that looks like it hasn't changed in centuries. Whether any particular scheme gets through is a question for the application itself, not the volume.
In practice, whether a house is listed decides nearly everything. An ordinary unlisted house, of which Battle has plenty, can often use permitted development rights for modest work. Those rights are narrower inside a National Landscape such as the High Weald, and they don't apply to listed buildings at all. Anything larger, or anything touching a listed property, needs a full application to the council. Before you exchange, ask your solicitor to confirm whether the house is listed and whether any earlier alterations were properly consented. Unconsented work on a listed building becomes the buyer's problem, and it's expensive to put right.
Your freedom to extend in Battle is middling. Unlisted homes have a workable route to a bigger house, and listed ones mean asking permission before you change almost anything.