Yes, but in the old parts of Hythe the people you most need to please have been dead for centuries. More than a hundred buildings are listed. Two conservation areas cover the historic core. The clay moves when the weather changes. Hythe says yes slowly, and in writing.
Historic England lists 132 buildings in Hythe: 3 at Grade I, 4 at Grade II* and 125 at Grade II. Listing covers the whole building, inside and out, so an extension, a new window or a removed wall needs listed building consent on top of any planning permission, and carrying out work without consent is a criminal offence, not a paperwork slip. Most of the list is Grade II, which is where ordinary homes sit, so this isn't only a problem for people who own churches.
There are 2 conservation areas in the area, Hythe and Saltwood. Inside them, the council controls demolition, work to trees and changes that alter the look of a street, and some alterations that would be permitted development elsewhere need a full application. Buyers who've extended a house somewhere else before tend to assume the same rules apply here. They find out otherwise when the paperwork arrives.
There are also 10 scheduled monuments in the area, among them stretches of the Royal Military Canal and parts of Saltwood Castle. That's the strictest tier of protection there is, and it only matters if your land runs up against one. If it does, get specialist advice before anyone starts digging.
The neighbours aren't put off. Across April 2024 to June 2026 the council logged 750 planning applications in the area, 310 of them in the last twelve months. Hythe residents alter their homes all the time. They just do it with a planning officer copied in.
The ground is the other conversation. The British Geological Survey rates shrink-swell clay here up to class 3, and about 78% of the area reaches that class or higher. Clay that swells when wet and shrinks when dry doesn't stop an extension, but it does affect the foundations: expect building control to want them deeper, pay for a structural engineer's view before you price the job, and check where the trees are before you decide where the extension goes.
In practice, a house outside the conservation areas that isn't listed can usually use permitted development for modest changes, subject to the national limits. A listed house, or one inside Hythe or Saltwood's conservation areas, should be treated as needing consent until the council says otherwise. Ask before you draw anything, not after the builder has booked a start date.
Your freedom to change a home in Hythe is limited: plenty of people get their extensions, but the town's history, and its clay, both get a say first.