You can, but the heritage rules and the ground both make it harder than the plain interwar streets suggest. Dozens of listed buildings sit within reach of the town. There are eight conservation areas nearby. The clay underneath every postcode moves with the weather. Most of the 1930s terraces are ordinary planning territory, and the extra work tends to come from the soil more than the paperwork.
Historic England's list puts 67 listed buildings in the area around Morden: three at Grade I, three at Grade II* and 61 at Grade II. The count covers a box wider than the district, so some are in neighbouring parts of Merton. Listing protects the whole building, inside and out, so even a modest change to a listed home needs listed building consent on top of any planning permission. Very few of the town's interwar terraces are affected by that, but anyone who owns one of the 67 will find the rules much stricter.
There are eight conservation areas within the same wider area, including Upper Morden, Dennis Park Crescent, Wandle Valley, John Innes (Merton Park) and Wimbledon Chase. Inside a conservation area, changes that would be routine elsewhere, such as front extensions, cladding, roof alterations and demolition, can need consent. Councils can also remove ordinary householder rights on particular streets with an Article 4 direction. Merton Council publishes conservation-area maps and any Article 4 directions on its planning pages. Check the exact street there, because the boundary can run between neighbouring roads.
There is one scheduled monument in the area, Morden Park Mound. It has the strictest protection of anything locally, but it only affects you if you own land right beside it.
People here do extend their homes, in large numbers. The council's planning register shows 796 applications between March 2024 and June 2026, 312 of them in the last twelve months. With interwar housing on every street, a planning officer in Merton will have dealt with your rear extension many times already.
The bigger issue for an extension is the ground. The British Geological Survey rates shrink-swell clay at class 3 across every postcode in Morden. Clay at that class swells when wet and shrinks when dry, so new foundations usually have to go deeper, especially near trees, and a structural engineer should look at the plans before a builder starts digging. That affects every house in Morden, whether or not it is in a conservation area.
Three listed buildings in the area are on Historic England's Heritage at Risk register. That means they are in poor condition and any repair will be closely examined, with grant funding sometimes available. It has no effect on the owner of an ordinary semi nearby.
In practice, a terrace or semi outside a conservation area can often add a modest rear extension or loft conversion under permitted development, through a prior-approval notice or with no application at all. A listed building, a home inside a conservation area, or a street covered by an Article 4 direction will need a full application. For every house, the clay means building regulations, foundation design and possibly a party-wall agreement will all take longer than the drawings.
The freedom to extend here is below average. Heritage rules affect some streets, the clay affects all of them, and an extension in Morden usually costs more in engineering than in planning.