You can, but expect to need permission for almost anything you do. Walworth has well over a hundred listed buildings. Conservation areas cover much of the map. Most homes are flats, which come with fewer automatic rights than houses do. Changing a home in Walworth means a lot of paperwork before any building starts.
Historic England lists 168 buildings in Walworth: one at Grade I, one at Grade II* and 166 at Grade II. Listing covers the inside of a building as well as the outside, so on any of those 168 a new window, a removed wall or a different front door needs listed building consent, and doing the work without it is a criminal offence. On these buildings, even small jobs need permission.
Twenty-three conservation areas fall within the map around Walworth. Inside one, the council controls demolition, works to trees and how changes look from the street, and householder rights that apply elsewhere can be narrower. Southwark Council can tell you whether a particular address is listed, inside a conservation area or both, and those two answers decide what you can do far more than the asking price does. Ask the council about the exact address before you start designing the kitchen.
Southwark Council received 556 planning applications in Walworth between April 2024 and June 2026, including 275 in the last twelve months. People here clearly do alter their homes. They just apply for permission first.
The ground under the whole district is rated class 3 for shrink-swell on the British Geological Survey's scale, and every postcode in the area reaches that class. Clay ground like this swells when it is wet and shrinks when it is dry, which matters for anything built on new foundations. This is mostly a question about how deep the foundations go. A structural engineer should look at it early, and building control will ask about it whatever the conservation officer thinks of the brickwork.
Three listed buildings in the area are on Historic England's Heritage at Risk register. That means they are in poor condition. Repairs to them may get grant funding and will get close scrutiny. For the owner of an ordinary flat down the road, this changes nothing.
In practice, the type of home matters as much as the heritage. Walworth is about 89% flats on the council-tax list, and flats don't get the householder permitted development rights that let a house owner add a modest rear extension or loft dormer without a full application. In a flat, anything structural also needs the freeholder's consent on top of the council's. The 9% of homes that are terraced houses have more room to change. Even then, a terrace inside a conservation area or on the listed register is back to applying for permission like everyone else.
If you want room to extend or alter, Walworth is one of the hardest places to get it. Most people here live with the home they bought and apply for permission whenever they want to change it.