Yes, though in much of Streatham you will be asking permission first. There are dozens of listed buildings. There are nineteen conservation areas in and around the district. The clay underneath moves. The neighbours are applying anyway, in their hundreds.
Historic England lists 76 buildings in and around Streatham: none at Grade I, 6 at Grade II* and 70 at Grade II. Listing covers the inside as well as the outside, so on a listed building almost any alteration, an extension included, needs listed building consent from Lambeth Council on top of planning permission. The absence of Grade I buildings is little comfort to the owner of one of the other 70.
There are 19 conservation areas in and around the district, among them Garrad's Road, Elderwood, Lancaster Avenue and Leigham Court Road (North). Inside a conservation area the council takes a closer interest in anything that changes how the street looks, from front extensions and roof alterations to materials, so a project that would go through quickly elsewhere can need a full application. Lambeth's conservation area map will tell you whether a particular house falls inside one, and it is the first thing to check on any home you want to enlarge.
The neighbours have not been put off. Between April 2024 and June 2026 there were 2,049 planning applications across Streatham, 865 of them in the last twelve months. That is a district full of Edwardian terraces where a large number of owners have looked at the back of the house and decided it could go further.
The ground needs as much thought as the paperwork. The British Geological Survey puts Streatham's shrink-swell hazard at class 3, and every postcode in the district reaches that class. Clay that shrinks in dry summers and swells in wet winters affects how deep foundations need to go, so a structural engineer's view on the foundations is part of the cost of any extension here, and a normal one.
Five listed buildings in and around the district are on Historic England's Heritage at Risk register. That means buildings in poor condition whose repair may attract grant support and will certainly attract scrutiny. It has no bearing on the buyer of an ordinary house down the road.
In practice, an ordinary house outside the conservation areas and off the listed register keeps the usual permitted development rights for modest extensions. Inside a conservation area, expect more of the work to need a full planning application, and on a listed building expect consent for nearly everything.
Freedom to extend is one of Streatham's weaker points. Plenty of people manage it, but a good share of the district makes you apply, wait and build deeper than you planned.