Usually yes, and the ground under the house will hold you up longer than the planners will. Heritage protection is concentrated in a few places. There is just one conservation area. Thousands of interwar semis have nothing protecting them from a loft dormer. The catch is clay, which turns the foundations of a rear extension into a conversation with an engineer.
There are 75 listed buildings in and around Eltham: 6 at Grade I, 16 at Grade II* and 53 at Grade II. Listing covers the whole building, inside and out, so any change that affects its character needs listed building consent on top of planning permission, and work done without it is a criminal offence. Most of those 75 are concentrated around the palace and the old core of the town. For a typical semi, they are someone else's problem.
The area has a single conservation area, Willersley Avenue and Braundton Avenue. Inside it, demolition, alterations to the front of a house and work on trees all get closer scrutiny from the Royal Borough of Greenwich, and the council expects changes to keep the street's character. Everywhere else, the rules are those of any ordinary suburban street.
Two scheduled monuments lie within the area, Eltham Palace among them. Scheduling is the strictest protection there is, and it only touches the land on and around the monuments. Unless you are digging footings beside the palace moat, it will not come up.
The Royal Borough of Greenwich logged 1,844 planning applications across Eltham between April 2024 and June 2026, and 729 of them in the last twelve months. That is a lot of people asking to change their houses, and most of them are fiddling with the back of a semi. Whatever extension you have in mind, a neighbour three doors down has probably already drawn it up, and a few will have built it.
The ground is the harder constraint. The British Geological Survey puts the whole area in shrink-swell class 3, a moderate hazard where clay soils expand when wet and shrink when dry. That doesn't stop an extension, but it does mean deeper foundations, a structural engineer's view on the soil and on any nearby trees, and a budget that allows for both. Look up the house's planning history and building-control records on the council's portal, because an older extension built on shallow footings is usually the first thing to show cracks.
Three listed buildings in the area are on Historic England's Heritage at Risk register. That means buildings in poor condition whose repair may attract grant funding and will certainly attract close attention. Unless you are buying one of them, it has no bearing on your plans, and if you are buying one, the repair bill is the extension.
For most of Eltham, permitted development rights cover the usual work: a modest rear extension, a loft conversion within set volume limits, an outbuilding in the garden. Anything in the conservation area, on a listed building or past those limits needs a planning application to the Royal Borough of Greenwich. Applying for a certificate of lawful development is the inexpensive way to confirm a project is permitted before the builders start.
The freedom to extend in Eltham is middling. Planning rarely gets in the way outside one conservation area and the palace grounds, but the clay under almost every house means a bigger project costs more to get out of the ground than it would on firmer soil.