Yes, and for most houses in Elsenham the process is fairly simple. Very few buildings are listed. No conservation area covers the village itself. Applications come in at a steady rate. The clay under the village will need more attention from your builder than the planners will.
Elsenham and its surroundings hold 33 listed buildings: one at Grade I, none at Grade II*, and 32 at Grade II. Listing protects the whole building, inside and out, and any work that changes its character needs listed building consent on top of any planning permission. Grade II is the commonest grade, and it still covers a replacement window. For the many homes in Elsenham that are not on the list, those rules do not apply.
Planning records show 1,060 applications in and around Elsenham between April 2024 and June 2026, and 507 of them in the most recent twelve months. That is plenty of evidence that people alter their homes here. In 2008 the government shortlisted Elsenham as a possible site for an entire eco-town, and next to that a single-storey rear extension is a small request.
The British Geological Survey puts the area's shrink-swell hazard at class 3, and 100% of the area reaches that class or above. Shrink-swell means clay ground that swells when it is wet and shrinks when it dries out, and the movement can crack shallow foundations. For an extension, that usually means deeper foundations, extra care near trees and a structural engineer's opinion before the plans are finished. It is an engineering cost, and the council's planners will not count it against you. Elsenham's clay will move under the extension whether or not it has planning permission.
With no conservation area inside the village boundary, an ordinary unlisted house usually keeps the permitted development rights that allow modest extensions without a full planning application, as long as the work stays within the national limits and the rights have not been removed on that property. Henham, also covered here, does have a conservation area, and rules there are stricter. A listed house needs consent regardless of size. The council's planning register lists previous applications for each address, and it is the quickest way to see whether the house you are considering has already been extended, refused or had its rights removed.
Elsenham gives homeowners a lot of freedom to extend. Listing applies to a small number of houses, and for most homes the main constraint is the clay foundations.