Yes, in most of Chessington you can. Hardly anything is listed. The houses are mostly interwar semis and terraces that no heritage body has ever looked at twice. The neighbours put in planning applications by the hundred. The heritage officer is rarely the obstacle here, and the clay underneath often is.
Historic England lists 19 buildings in and around Chessington: none at Grade I, 1 at Grade II* and 18 at Grade II. Listing covers the whole building, inside and out, and almost any change to one needs listed building consent on top of planning permission. With 19 across a suburb of family houses, the chance of buying one without knowing it is small, and the conveyancing searches will flag it if you do.
Four conservation areas fall in and around Chessington: Horton, Long Grove, The Manor and West Park. Inside them the council takes a closer interest in anything visible from the street, including side extensions, roof alterations, front boundaries and some tree work, and some changes that would go through automatically elsewhere need an application. A side extension on a semi in Hook goes through the ordinary process, and the same plan inside The Manor gets read for its brick and its roofline.
There is one scheduled monument in the area, the Castle Hill earthwork. Scheduling is the strictest protection there is, and it matters only to the few gardens and plots that border the site.
Kingston upon Thames received 541 planning applications for Chessington between April 2024 and June 2026, 230 of them in the last twelve months. That is a suburb where altering the house is normal, and the council's planning register will show what has already been built on any street you are looking at, so you can see whether the side extension you want has a precedent next door.
The ground is the constraint people forget. The British Geological Survey rates the whole of Chessington at class 3 for shrink-swell, and every postcode reaches it: clay that swells when wet and shrinks when dry. For an extension that usually means deeper foundations than a builder's first quote allows for, and a structural engineer's view, especially near large trees, whose roots dry the clay. Ask the surveyor to check for movement cracks in the existing house and to note how close the nearest big tree is, because the original 1930s foundations have had decades on this clay to show their weak points. The scheduled monument is old, but the clay is the thing that will shape your extension.
In practice, a house outside the listed buildings and the four conservation areas usually keeps the standard householder rights to build at the back and in the roof without a full application, within national size limits. Flats do not have those rights, and a lawful development certificate from the council is the cheap way to confirm a project qualifies. Anything bigger, or anything inside a conservation area, goes through the normal application process.
You have a middling amount of freedom to extend in Chessington: the heritage rules leave most homes alone, but the conservation areas and the clay mean not every plan goes through easily.