For most homes in Cam, yes. The heritage rules hit hard in a few places and hardly at all in the rest. Most of the housing is post-war, and the planning system treats it as ordinary. Listed buildings are few and spread across a wide area, and there is only one conservation area. Neighbours file extension plans at a steady rate. The trouble is mostly for the few who buy something old.
The wider area around Cam has 60 listed buildings: one Grade I, six Grade II* and 53 Grade II. Listing protects the whole building, inside as well as out, so on a listed home you need listed building consent from the council for almost any change that affects its character. That covers windows, walls and interiors, on top of any planning permission. Grade II is the commonest grade, and still strict. The Grade I is in a different league altogether, so nobody is getting a dormer onto that one. On the valuation list, about 16% of Cam's homes date from before 1930. Listing is concentrated among that older minority, and most buyers will never deal with it.
There is one conservation area in the wider area, Stinchcombe. Inside a conservation area the council can control changes it would let pass elsewhere, such as demolition, work on trees and alterations that affect how the street looks, so some projects need consent there that would go ahead without it on an ordinary road. Outside Stinchcombe, that layer of control doesn't apply.
Plenty of Cam's residents do extend. The planning register for the area shows 586 applications between April 2024 and June 2026, and 257 of them in the last twelve months. Those figures count requests only. They say nothing about how many were approved. A village where three bedrooms is the norm keeps putting in paperwork for a fourth.
For the typical Cam house, the main question is whether the job is permitted development or needs a full application. Permitted development rights let a householder carry out some extensions without applying. They do not apply to listed buildings, they are narrower inside conservation areas, and on some newer estates a condition of the original permission removed them. Ask Stroud District Council whether permitted development rights still apply to the specific house, and whether any condition took them away when it was built. That one answer decides whether a rear extension needs a full application or just a builder.
Freedom to extend in Cam is middling. For a standard post-war family house it is close to the national norm, and much tighter for the small number of listed homes and those in Stinchcombe.