You can, though the council will have more say in the result than you will. Listed buildings run into the hundreds. There are dozens of conservation areas. There is clay under every postcode. Getting what you want here takes paperwork and patience.
Historic England lists 526 buildings in and around Chiswick: 19 at Grade I, 24 at Grade II* and 483 at Grade II. Listing protects the whole building, inside and out, so changing a staircase, a fireplace or a window in a listed house needs listed building consent on top of any planning permission. Grade II is the most common grade and also the one ordinary buyers most often end up owning. Most of the 483 are houses on residential streets.
There are 29 conservation areas in and around the district, including Bedford Park, Turnham Green, Strand on the Green, Old Chiswick, the Glebe Estate and the stretch along Chiswick High Road. Inside a conservation area the council takes a close interest in anything visible from the street, including roof extensions, front walls, windows and the loss of trees. The Dukes of Devonshire left Chiswick House in 1929 and their family names are still on the street signs all over the district. The planning rules have been just as hard to shift.
There is one scheduled monument in the area, the highest level of protection there is. It mainly concerns land next to it, not the typical terrace.
People here are extending all the time. Hounslow council received 2,403 planning applications for the area between February 2024 and July 2026, 979 of them in the last twelve months. Whatever you are planning, someone on the same street has probably already applied for it, and the council's online planning register will show how that went. Read it for the street before you budget for the loft.
Under all of it is clay. The British Geological Survey puts the area's shrink-swell hazard at class 3, and every postcode in Chiswick is rated at that level or above. Clay that shrinks in dry summers and swells in wet winters moves foundations, especially near large trees, so an extension here usually needs deeper footings and a structural engineer's opinion before the builder starts. The structural engineer's fee is a cost a buyer here should expect, though the clay is no cause for alarm.
Twelve listed buildings in and around Chiswick are on Historic England's Heritage at Risk register. That means they are in poor condition, and their repair can attract grant money and will attract close scrutiny from Historic England. They are no danger to anyone buying an ordinary house down the road, though they are a large commitment for anyone who buys one of them.
In practice, the permitted development rights that let owners elsewhere add a modest rear extension or a dormer without a full application are narrower in a conservation area and do not apply to listed buildings in the usual way. Ask Hounslow council, or Ealing for the Bedford Park and Acton Green end of W4, whether the house is listed or inside a conservation area. The answer will tell you whether a job can go ahead under those rights or needs a full application.
Chiswick gives an owner very little freedom to change a house. The house you buy is likely to be close to the house you end up with.