Yes, and the heritage rules are lighter here than a stretch of riverbank this grand would suggest. There are only three listed buildings. There is no conservation area. The neighbours send in planning applications all the time. The clay and the countryside designation will give you more to think about than the heritage officer will.
Greenlands has 3 listed buildings: 0 at Grade I, 1 at Grade II* and 2 at Grade II. Listing covers the whole building, inside and out, so any change that affects its character, from windows to internal walls, needs listed building consent on top of any planning permission. Grade II* is the smaller, more significant tier, and it attracts closer scrutiny. With three listed buildings in the whole area, the odds are good that the house you're looking at isn't one of them, but check the individual address rather than assuming. There is also no conservation area inside Greenlands, so the extra controls on demolition, trees and external details that come with one don't apply here.
Plenty of people do build here. The planning data for the area records 1,927 applications between April 2024 and June 2026, with 852 in the last twelve months. That's steady evidence that people alter homes around here, and that the planning department sees a lot of kitchen extensions. It says nothing about how many were approved, so read your neighbours' applications for guidance, not as a promise.
The ground deserves more attention than the heritage record. The British Geological Survey puts shrink-swell risk at class 3 across 100% of the area, meaning clay that swells when wet and shrinks when dry. For an extension, that usually means deeper foundations and a structural engineer who takes nearby trees seriously. Soluble rock is also at class 3 across the whole area, which is another reason to have the ground investigated before you dig. Neither needs to put you off. It just means the foundations for your garden room may cost more than you expected.
In practice, many smaller rear extensions and loft changes can go ahead under permitted development without a full planning application, as long as the house isn't listed and the rules for your particular property type are met. The complication is the landscape. The whole of Greenlands sits inside the Chilterns Area of Outstanding Natural Beauty, where some permitted development rights are tighter than in an ordinary suburb, so check with Buckinghamshire Council before you assume a project is exempt. A lawful development certificate costs less than an argument afterwards.
Freedom to extend is one of Greenlands' real strengths. Heritage controls barely touch most homes here, and the things that need planning are the clay under the house and the countryside around it, not the listed buildings.