Yes, and with less fuss than in most of London. There are no conservation areas. The listed buildings could be counted on a pair of hands and a few toes. The neighbours file for extensions all the time. The clay under the house is a harder obstacle than the planning department.
Historic England lists 17 buildings in and around Upper Edmonton: none at Grade I, one at Grade II* and 16 at Grade II. Listing covers the inside of a building as well as the outside, so any change that affects its character, from a window frame to an internal wall, needs listed building consent from the council. With 17 in the area, most buyers will never own one, and the area has no conservation areas and no scheduled monuments. Almost every terrace here is an ordinary house under ordinary planning rules.
Between April 2024 and June 2026, 694 planning applications were lodged for the area, 366 of them in the last twelve months. That is a steady stream of residents doing to their houses what a new buyer is planning to do to theirs. Whatever extension you have in mind, someone on a nearby street has probably already applied for something like it.
The ground needs more thought than the paperwork. The British Geological Survey rates the area at class 3 for shrink-swell clay, and every part of Upper Edmonton reaches that class. Clay of this kind swells when wet and shrinks when it dries out, so an extension needs foundations deep enough to sit below that movement. Trees near the new walls make the problem worse. A structural engineer will want to see the ground before the builder quotes for the foundations, and building control will expect a design that allows for it. Planners are unlikely to object to your extension here, but the clay will make its views known.
Three of the area's listed buildings are on Historic England's Heritage at Risk register. That means they are in poor condition and in need of repair, which can bring grant money and will bring close attention from Historic England and the council. It is a matter for the owners of those three buildings. A buyer of an ordinary terrace nearby is unaffected.
For a typical house, a modest rear extension or a loft conversion may fall under permitted development, which lets householders build within set limits without a full planning application. Anything larger, or anything on a flat, will need permission. Flats do not carry the same householder rights, which matters in an area where so many homes are flats. Ask Enfield Council whether an Article 4 direction removes permitted development rights on the street you are buying in, because a single direction can make the difference between a straightforward build and a full application.
Freedom to change the house is one of Upper Edmonton's real strengths. Heritage rules will rarely stop you, so the main things to plan around are the clay, the budget and the neighbours you share a wall with.