Mostly yes, and the neighbours are already at it. Listed buildings are few, and none are top grade. Two conservation areas cover the old core. Hundreds of planning applications go in every year. Here the obstacle is more likely to be the clay than the council.
Historic England lists 85 buildings in Caversham. None is grade I, three are grade II* and 82 are grade II. Changing a listed building, inside or out, needs listed building consent on top of any planning permission, and that can cover windows, fireplaces and internal walls you might assume were yours to change. Out of all Caversham's homes, 85 is a small number. If the house you're buying is one of them, the survey will tell you well before the builder does.
There are two conservation areas, St Peter's and Surley Row, both around the older parts of Caversham near the twelfth-century Church of St Peter. Inside them, the council takes a closer interest in how a house looks from the street, so extensions, roof changes and the removal of trees and walls get more scrutiny than they would elsewhere. Outside those two areas, the post-war semis and detached houses that make up most of Caversham come without that extra attention.
Evidence that people extend here is easy to find. Between September 2023 and June 2026 there were 1,267 planning applications, 572 of them in the last twelve months. That's the paperwork trail of kitchens knocked through, lofts converted and side returns filled in. Before you make an offer, look up the applications on the street you're buying into. It's the most honest description of the neighbourhood's plans you'll get, and considerably more detailed than the sales particulars.
The ground needs more thought than the paperwork. The British Geological Survey puts Caversham's shrink-swell hazard at class 3, and 100% of the area reaches that class. Clay that swells in wet winters and shrinks in dry summers moves foundations, so a new extension may need deeper footings than a builder's first quote assumes, and trees near the footprint matter. Get a structural engineer to look before you sign off the design. It's cheaper than calling one out once a crack has appeared.
In practice, most homes outside the two conservation areas and away from the listed buildings can use permitted development rights for modest rear extensions and loft conversions, subject to the usual size limits. Inside the conservation areas, or in a listed building, assume you'll need consent and plan for the time that takes. Either way, check with Reading's planning department on the specific address before you instruct an architect.
Your freedom to extend here is middling. The heritage rules touch only a small part of Caversham, but clay, conservation areas and a busy planning register mean few projects are simple.