Yes, extending a home in Stokenchurch is usually straightforward. The village has few listed buildings. There is a single conservation area, around the commons. Most of the housing went up after the war and carries no special protection. Outside the old centre, the planners have little to protect you from.
Stokenchurch has 8 listed buildings. None are Grade I, 1 is Grade II* and 7 are Grade II. Listing covers the inside of a building as well as the outside, so even small changes such as new windows, an opened-up wall or a replaced staircase need listed building consent, on top of any planning permission. Eight buildings out of a whole village is a short list. A village that made its living building chairs has kept very little the state wants frozen in place.
There is one conservation area, Stokenchurch itself, designated in 1989 around the centre of the village, where large commons run along both sides of the main road. Inside it, alterations to the outside of a home are judged partly on how they look from the common, demolition needs consent, and work to trees needs notice. Check Buckinghamshire Council's map to see whether a particular house falls inside the boundary, because two houses facing the same common can sit under different rules.
Buckinghamshire Council's planning register logged 693 applications in the Stokenchurch area between April 2024 and June 2026, 311 of them in the last twelve months. That is a village that keeps building onto itself. Any planning agent working the area will have seen the side extension you have in mind several times already.
Every postcode in the village also falls within the Chilterns Area of Outstanding Natural Beauty, which can narrow what counts as permitted development and how far an extension can go without a full application, so ask the council before assuming the national allowances apply. Outside the conservation area and away from the listed buildings, a post-war semi is treated much like a post-war semi anywhere else in Buckinghamshire. The protected landscape asks for some care about how things look, and the conservation officer has far less say on most of these streets.
For most homes in Stokenchurch, extending is a fairly ordinary job, and the planning rules only tighten for the handful of houses around the commons.