Yes, and on most streets heritage rules won't get in your way. A dozen listed buildings. Two conservation areas. Hundreds of planning applications a year from neighbours doing the same thing. The thing to worry about is the clay under the house, not the conservation officer.
Historic England's list covers 12 buildings in and around Greenhill: none at grade I, one at grade II* and 11 at grade II. Listing protects the whole building, inside and out, so any change that affects its character needs listed building consent on top of any planning permission, and doing the work without it is a criminal offence rather than a paperwork mistake. With 12 listed buildings in a suburb this size, the odds of owning one are low, and anyone who does will have been told at the conveyancing stage, or should ask their solicitor why not.
Two conservation areas touch the area: Eddington, Herne Bay and Herne Windmill. Inside a conservation area, the rules on what you can do without applying tighten up, and changes that alter the look of a street get more scrutiny from the council. Outside them, which describes most of Greenhill's post-war semis and bungalows, the heritage layer barely exists.
The neighbours clearly aren't put off. Across the planning records from April 2024 to June 2026, 807 applications were lodged for the area, with 350 of them in the last twelve months alone. That's live evidence of people adding rooms, converting lofts and changing what they bought, and it means an application here is routine, not an event.
The ground is where the real homework lies. The British Geological Survey places every postcode in the area at class 3 for shrink-swell clay, a published hazard class that describes soil which swells when wet and shrinks as it dries. For an extension, that means foundations may need to go deeper than the builder's first quote assumes, especially near trees, and a structural engineer's view before the plans are finalised is money well spent. It isn't a reason to panic. It's a reason not to let the cheapest quote dig the footings.
In practice, many single-storey rear extensions and loft conversions on houses can go ahead under permitted development rights, without a full planning application, provided they stay within the size and design limits. Flats and homes in a conservation area have fewer of those rights, and a listed building has none worth relying on. Canterbury's planning team will confirm what your particular house can do, and a lawful development certificate is cheap insurance before a buyer's solicitor asks the same question years later.
Greenhill gives you a fair amount of freedom to extend: middling rather than generous, with few heritage rules for most homes but ground that asks for proper foundations and a couple of conservation areas that tighten the rules where they apply.