Yes. In most of Caterham, extending a house is a normal planning job, and your neighbours are already doing it. Very few homes are listed. There are three conservation areas. Planning applications come in by the thousand. The ground is more likely to limit an extension than the heritage rules are.
Caterham has 26 listed buildings. One is Grade I, none are Grade II*, and 25 are Grade II. Listing covers the whole building, inside and out. Almost any change that affects its character, from windows to walls to an extension, needs listed building consent on top of any planning permission, and doing the work without it is a criminal offence. Most of these buildings are old churches, houses and a pub around the historic core on the hill. Unless you're buying one of them, listing won't affect you.
Three conservation areas fall in and around the town: Caterham Barracks, Kenley and Kenley Aerodrome. Inside them, the council also weighs how a change affects the look of the area, and some work that needs no application elsewhere can need one there. If the house sits in one of them, check with the council what applies before committing to a design.
There are three scheduled monuments in the area, including an Iron Age hillfort at War Coppice Camp. That's the strictest protection there is, but it only matters if your land borders one.
Between April 2024 and June 2026, the planning data recorded 4,011 applications in the area, 1,719 of them in the last twelve months. That shows people here are altering their homes all the time. It says nothing about how many were approved.
The geological survey classes about 49% of postcodes as shrink-swell class 3 or above, the highest class found here. That means clay which swells when wet and shrinks when dry, and it can move foundations that aren't dug deep enough. It doesn't stop an extension, but it can make one cost more. Get a structural engineer's view on foundation depth before you settle the budget, especially where the extension will be near large trees.
Outside the listed buildings and conservation areas, plenty of rear extensions, loft conversions and outbuildings can go ahead as permitted development without a full planning application, within the national size limits. Anything bigger, or anything on a listed building or in a conservation area, goes through the council. Ask the council before assuming, and get a lawful development certificate if you plan to sell later.
Your freedom to extend in Caterham is middling: few homes are listed, but check whether you're in a conservation area and allow for the clay.