Yes, in most cases, because heritage rules hardly touch Thamesmead East's houses. The few listed buildings nearby are in the wider area, not among the post-war terraces. There are five conservation areas nearby, but they cover other streets. Dozens of neighbours have applied to change their homes. The ground is the harder part, because the clay here moves.
Taking in the wider area around Thamesmead East, there are 10 listed buildings: none at grade I, 2 at grade II* and 8 at grade II. Listing covers the whole building, inside and out, and almost any alteration needs listed building consent on top of planning permission. Fewer than one in a hundred homes in Thamesmead East was built before 1930, so few of them are old enough to have caught a listing inspector's eye.
The same wider area has 5 conservation areas: Brook Street, Erith Riverside, Erith Road, Lesney Park Road and Woolwich Road. Inside a conservation area the council has tighter control over changes to the outside of a building. Bexley Council publishes the boundaries, so check them for the address you're looking at. Two of the five are named after Erith, which tells you where most of the protected streets are.
There is 1 scheduled monument in that wider area, the strictest tier of protection, and it matters only for work on or right next to the monument itself.
Bexley Council's planning register shows 32 applications for the area between May 2024 and May 2026, 11 of them in the last twelve months. Neighbours here do apply to change their homes, and the register shows what each of them asked for.
The ground is the bigger problem. The British Geological Survey rates the area's shrink-swell hazard at class 3, a moderate rating, and every postcode in Thamesmead East reaches it. Clay that swells when wet and shrinks when dry pulls at shallow foundations, so an extension here usually needs deeper footings and a structural engineer's view, especially near trees. The planning rules here are relaxed, but the clay is not.
Outside listed buildings and conservation areas, many single-storey rear extensions and loft changes to a house can go ahead under permitted development rights, without a full planning application, within national size limits. Flats don't have the same rights, and about four in ten homes in the area are flats, so a flat owner should expect to apply for permission and to get the freeholder's agreement. For a house, the usual first step is a lawful development certificate from the council, which confirms the work is allowed.
The freedom to extend here is about average. Heritage rules rarely get in the way, but the clay and the large share of flats keep it from being easy.