Usually yes, and how easily depends on which Greenhithe you buy in. The old village by the river is a conservation area with listed buildings around it. The newer estates carry almost none of that. The neighbours apply for planning permission at a steady rate. The ground needs checking more than the paperwork does.
There are 72 listed buildings in and around the Greenhithe area: two Grade I, three Grade II* and 67 Grade II. Listing covers the whole building, inside and out, so a new window, a knocked-through wall or a rear extension on one of them needs listed building consent from Dartford Borough Council on top of any planning permission, and doing the work without it is a criminal offence. Most buyers here will never own one, but the people who do should expect conversations about mortar.
Two conservation areas fall in and around the area, one of them Greenhithe itself and the other Dartford Town Centre. Inside a conservation area the council takes a closer interest in anything visible from the street, from extensions and roof changes to the demolition of a garden wall. The Greenhithe conservation area takes in the old riverside village, the part of the place that grew up around a landing place and some chalk wharves. Waterstone Park, put up in the Thames Gateway years, was designed by people who expected the residents to add a conservatory and not to ask anyone first.
The neighbours are certainly busy. Between April 2024 and June 2026 there were 210 planning applications in the Greenhithe area, 89 of them in the last twelve months. Those are applications, not approvals, and they cover everything from rear extensions to changes of use, but they show that altering a home here is a normal thing to try. Search the council's planning register for the street you are looking at, because an application next door tells you what the planning officers have already been asked about.
The British Geological Survey rates the ground in the area up to class 3 for shrink-swell, and about 23% of the area reaches that level. That class means clay that swells when wet and shrinks when dry, which can move shallow foundations, especially near trees. In practice an extension on that ground may need deeper footings than the builder's first quote assumes, and a structural engineer's view at the design stage costs far less than fixing cracks later.
On most ordinary houses outside the conservation area, a modest rear extension or loft conversion may fall under permitted development, which means no planning application is needed, though the rules on size are strict and a lawful development certificate from the council is the safe way to confirm it. Flats have no permitted development rights at all, and with about 41% of homes in the area being flats, a large share of owners will need full permission plus their freeholder's consent for almost anything structural. The flat buyer's real planning authority is often the lease.
Greenhithe gives you a middling amount of freedom. The estates are relaxed, the riverside village is not, and the clay underneath both deserves a proper look.