Yes, you can extend in Dulwich, but you'll need permission for more of it than in most of London, and the ground needs its own survey. The listed buildings run into the hundreds. Conservation areas cover large parts of it. Every postcode is on clay that moves. Neighbours keep extending anyway, and you can follow every case on the planning register.
Historic England's list has 194 listed buildings in and around Dulwich. One is grade I, 15 are grade II* and 178 are grade II. On a listed building, changes inside and out that affect its character need listed building consent, on top of any planning permission, and that can include windows, internal walls and even the paint on some surfaces. Most homes in Dulwich aren't listed. The ones that are come with a long history of decisions that you take on with the deeds.
There are 13 conservation areas in and around Dulwich, including Dulwich Village, Dulwich Wood, Herne Hill, Park Hall Road, Lancaster Avenue and Elderwood. Inside them, demolition, some extensions and work visible from the street need consent that wouldn't be needed elsewhere, and the council judges whether a proposal preserves the character of the area. Two houses on neighbouring streets can face very different rules. Find out which side of the line your house is on using Southwark Council's conservation area maps, and do it while you're still deciding whether to buy.
The rules haven't stopped people. The planning register records 897 applications in Dulwich between April 2024 and June 2026, and 395 of those were in the last twelve months. Plenty of people still extend here. They just start by commissioning drawings.
The ground needs as much attention as the paperwork. The British Geological Survey gives Dulwich a shrink-swell class of 3 for clay that swells when wet and shrinks when dry, and every postcode in the area reaches that class. For an extension, that means deeper foundations than you might expect, extra care near trees, and a structural engineer's opinion before you set a budget. Clay this widespread is a cost to plan for, not a reason to panic. In Dulwich the ground moves more than some of the planning rules do.
Four listed buildings in and around the area are on Historic England's Heritage at Risk register. That means buildings in poor condition, whose repair may qualify for grants and will be watched closely by the authorities. It's a matter for their owners and won't affect the buyer of an ordinary house down the road.
In practice, some smaller works on an unlisted house outside a conservation area may count as permitted development and need no planning application. Inside a conservation area or on a listed building, that freedom shrinks, and side extensions, roof changes and new windows are where buyers most often find they need consent. A lawful development certificate from the council confirms that a project needs no planning permission, and in Dulwich it is cheaper than finding out the hard way.
Dulwich gives you less freedom to change a house than most of London does. The work can be done, but the conservation areas and the clay both need dealing with first.