Usually yes, but you'll deal with more paperwork than you'd expect for a seaside bungalow. Five conservation areas cover the older parts of the area. Dozens of buildings are listed. The neighbours apply for planning permission all the time. Owning the house doesn't mean you get the final say on it.
The surrounding area has 53 listed buildings: 2 at Grade I, 3 at Grade II* and 48 at Grade II. Listing covers the whole building, inside and out, so knocking through a wall, changing the windows or adding a rear extension needs listed building consent on top of any planning permission. Do the work without consent and the council can make you undo it at your own cost. The post-war stock that makes up most of Dymchurch is mostly unlisted, so for most buyers this only matters if they fall for one of the older buildings.
There are five conservation areas in the wider area: Dymchurch High Street; Dymchurch, Church Area; New Romney, Cannon Street; Newchurch; and Old Romney. Inside one, changes to the front of a house, its roofline and its boundaries get closer attention from the council, and some work that needs no permission elsewhere may need it there. An estate agent's "scope to extend" was written by someone who never has to fill in the form.
There are also 7 scheduled monuments nearby, the strictest level of heritage protection, including Dymchurch Redoubt and Martello tower no 24. They matter mainly if your land is near one.
Your neighbours aren't put off. Between April 2024 and June 2026, 3,084 planning applications were logged across the wider area, 1,339 of them in the last twelve months. Plenty of people here try to change their homes, and the council has a steady flow of them to deal with. How many were approved is a separate question that these figures don't answer.
In practice, check three things before you draw anything up. First, whether the house is listed. Second, whether it's inside a conservation area. Third, whether the work falls within permitted development, the national rules that let you do some extensions without a full planning application. Ask the council, or pay for a pre-application view, instead of taking the seller's word for it. Almost the whole area is also in the Environment Agency's highest flood zone, so any application should expect questions about flooding. A single-storey extension on the Marsh is a flood conversation as well as a design one.
Freedom to extend here is below average, and it's the paperwork that holds you back more than the neighbours: listing and conservation rules around the older core, and the flood zone almost everywhere. The unlisted post-war bungalow is the easiest place to start. Everything older needs more patience and a better architect.