You can, but in Greenwich an extension usually means asking permission from people with long memories. The area has hundreds of listed buildings. The ground under all of it shrinks and swells. The neighbours keep the planning department busy. Most of what you would want to build gets a hearing, and you should not expect it to be a quick one.
There are 361 listed buildings in the area. Eighteen are grade I, 21 are grade II* and 322 are grade II. Listing protects the whole building, inside and out, so replacing windows, removing a wall or changing a staircase in a listed home can each need listed building consent before work starts. The particulars may say "period features", and if the house is listed those features are protected by law and the owner cannot simply remove them.
There are four conservation areas within the mapped area around Greenwich. A conservation area gives the council closer control over demolition, work to trees and changes that alter how a street looks, so a project that would be routine elsewhere can need a full application inside one. Look up the house on the Royal Borough of Greenwich's maps of listings and conservation areas while backing out is still cheap. Two homes on the same street can come under very different rules.
Nine scheduled monuments sit in and around the area, including the Romano-Celtic temple and the Anglo-Saxon cemetery in Greenwich Park. They are the strictest tier of protection and matter mainly to anyone digging nearby. Around Greenwich Park, the Romans and the Anglo-Saxons got there first.
Plenty of people still try. The Royal Borough of Greenwich logged 1,480 planning applications here between April 2024 and June 2026, 672 of them in the last twelve months. People in Greenwich clearly alter their homes, and for most of them it starts with a form.
The British Geological Survey rates the ground across the whole area at class 3 for shrink-swell, the moderate band, which means clay that swells when wet and shrinks in a dry summer. For an extension, that usually means deeper foundations and a structural engineer's view on the design, and trees near the footings matter more. Building control will want to see it covered.
Three listed buildings in the area are on Historic England's Heritage at Risk register. They are buildings in poor condition that may qualify for repair grants and will be closely scrutinised. They have no effect on an ordinary house nearby, but they are a reminder that conservation officers take an interest in every repair.
Flats make up most of the homes in Greenwich, and flats don't get the permitted development rights that houses have, so almost any change to a flat starts with an application. A house away from the listed buildings and outside the conservation areas will have more freedom. Even so, the clay and the council will both want a say.
Your freedom to extend in Greenwich is limited. A modest, well-designed project usually gets through, and an ambitious one needs patience, a good architect and someone who enjoys paperwork.