Yes, and your neighbours are already doing it. Most homes aren't listed. Four conservation areas cover the older corners. The clay underneath matters more than the paperwork. Getting permission in Cobham is the manageable part, and the ground is the harder negotiation.
Historic England lists 77 buildings across Cobham: one at Grade I, 5 at Grade II* and 71 at Grade II. For those buildings, almost any change that affects their character, inside or out, needs listed building consent from Elmbridge on top of any planning permission, and doing the work without it is a criminal offence. Against a housing stock dominated by post-war and later detached houses, 77 is a small number. If yours is one of them, every window, chimney and internal wall is a conversation with the council.
There are four conservation areas: Cobham, Cobham Plough Corner, Cobham The Tilt and Stoke D'Abernon. Inside them, some changes that would go ahead without permission elsewhere need consent instead, including some extensions, cladding and demolition, and works to trees need advance notice. The boundaries follow the old village cores, around the church, the mill and the old coaching road, which is where the oldest houses are. The newer detached streets towards the station and the heath mostly fall outside them.
Elmbridge's planning register shows how busy the area is. Across the Cobham area, 3,614 applications were lodged between April 2024 and July 2026, and 1,520 of them in the last twelve months. That is the live record of people building, extending and reworking what they bought. In Cobham, the house you buy is often treated as a starting point.
The ground deserves more attention than the paperwork. The British Geological Survey gives shrink-swell clay a class 3 hazard rating at its highest here, and about 62% of the area reaches that class or above. Clay of that kind swells when it's wet and shrinks when it's dry, so extensions usually need deeper foundations than they would on sand or chalk, especially near large trees. That means a structural engineer's report and a building-control conversation, not a reason to give up. The other ground hazards on the same survey are at their lowest classes, and radon is in the lowest band. The clay under Cobham doesn't care how good your architect is, so find out about it before you sign off the drawings.
In practice, for an unlisted house outside the conservation areas, many single-storey rear extensions and loft conversions can go ahead under national permitted development rights, within size limits, without a full planning application. Inside a conservation area those rights shrink, and on a listed building they hardly apply at all. Ask Elmbridge for a lawful development certificate for anything you plan to build without permission, so you have the council's confirmation in writing before a single trench is dug.
Freedom to extend is middling here. Most houses can grow without much fuss, but the listed buildings, the four conservation areas and the clay mean that how hard it is depends on exactly which house you buy.