Yes, and in most of Eastchurch nobody's heritage department will stand in your way. There are no conservation areas. Listed buildings are a small handful. Neighbours put in planning applications all the time. The clay under the house is a tougher negotiator than the council.
This page covers Eastchurch together with Warden and Leysdown-on-Sea, three settlements in one ward on the Isle of Sheppey. Historic England lists 22 buildings across the area: one Grade I, three Grade II* and 18 Grade II. Listing covers the whole building, inside and out, so changes to one need listed building consent on top of any planning permission, and replacing windows or knocking through a wall becomes a conversation with the council. For the thousands of post-war bungalows and houses that aren't on the list, none of that applies.
The area also has three scheduled monuments, the strictest tier of protection in England. They matter mainly if your land borders one, where even groundworks can need consent.
What the neighbours are doing tells you more than the rules do. Between April 2024 and June 2026, 543 planning applications were lodged across the area, 219 of them in the most recent twelve months. That's not a place where people are frightened of the planning portal. Extensions, conversions and loft rooms go in all the time here. Whether any one application succeeds depends on the scheme, and nobody should take the volume as a promise of approval.
The ground is where the real homework is. The British Geological Survey places every postcode in the area at class 3 for shrink-swell, which is its measure of clay that swells when wet and shrinks when dry. The same mapping puts every postcode at class 3 for compressible ground, and 99% for running sand. None of that stops you extending. It means foundations may need to go deeper than a builder's standard quote assumes, and a structural engineer should see the site before anyone digs. The cheapest extension is the one that doesn't need underpinning three years later.
For an ordinary house outside the listed few, with no conservation area to tighten the rules, a modest extension may fall within permitted development, which needs no full planning application. Flats and listed buildings don't get the same freedom. Check the specific property with Swale Borough Council before commissioning drawings, because permitted development has limits that estate agents tend to round up to "potential to extend".
Your freedom to extend here is middling: the heritage rules are light, but the ground adds cost and paperwork to almost any extension. Budget for the engineer before you budget for the kitchen.