Yes, you can extend a house in Swanscombe, and there is very little heritage paperwork. The town has four listed buildings. It has no conservation areas. Your neighbours are already busy extending. The clay underneath is the part that pushes back.
Only 4 buildings in Swanscombe are listed: 1 at grade I, 1 at grade II* and 2 at grade II. Listing means almost any change to the building, inside or out, needs listed building consent on top of any planning permission, and doing the work without it is a criminal offence. That only matters if you buy one of those four. There are no conservation areas and no scheduled monuments in Swanscombe itself. The nearby conservation areas are in Greenhithe, Southfleet and parts of Northfleet, so the strictest rules in the area cover the towns next door.
From April 2024 to June 2026, 86 planning applications were lodged in Swanscombe, 38 of them in the last twelve months. That counts what people applied for and says nothing about how many were approved. It does show that changing a house here is a normal thing to do. A letter about the neighbour's plans is a regular piece of post in Swanscombe.
The British Geological Survey puts Swanscombe's shrink-swell hazard at class 3, and 100% of the area reaches that class. Shrink-swell clay swells when it is wet and shrinks when it dries, and a new extension can move differently from the original house beside it. In practice that means deeper foundations, more care near trees, and a structural engineer's report before the builder prices the groundworks. The ground here has been dug into before. The deneholes cut into the chalk along this stretch of the Thames were here centuries before the houses. A modern extension only needs a deeper trench than the original house had.
Many single-storey rear extensions and loft conversions on houses can go ahead under permitted development rights, without a full planning application. Flats don't have the same householder rights, and the rights can be removed from individual properties by condition or direction. A lawful development certificate from Dartford Borough Council will confirm in writing that a scheme counts as permitted development. Get one before you pay a builder, and expect any extension on this clay to need building control approval for its foundations as well.
Extending a home is one of the things Swanscombe makes easiest. Planning gives you a lot of room, and the main limit is how deep the foundations need to go.