Yes, and with fewer people in a heritage office telling you no than most towns manage. Patchway carries no conservation area within its boundary and no scheduled ancient monuments, so the heavyweight constraints that tie up alterations elsewhere are simply not present. The listed buildings that do exist number around 25 across the wider area, and none of them is likely to be the ordinary post-war semi you have in mind. For the large majority of homes here, the rules are the standard national ones with nothing extra bolted on. That makes the town an easier place to build a rear extension than almost anywhere with a prettier reputation.
The listed stock is small and tightly concentrated. Of the roughly 25 listed buildings in the area, none sits at the top grade, three hold the middle two-star grade, and the remaining couple of dozen are the standard lower grade. Listing matters enormously if you happen to own one, because it drags almost any change, inside or out, into needing formal consent, and it takes no interest in how reasonable your plans are. But listed properties are a sliver of the housing here, and the town's dominant stock of post-war houses is overwhelmingly unlisted. Unless the paperwork on your specific address says otherwise, the heavy heritage rulebook belongs to someone else.
In practice most owners here operate under permitted development, the national allowances that let you add a modest rear extension, convert a loft, or make similar changes without a full application, as long as you stay inside the limits. Overshoot those limits and you apply for planning permission like anyone else, and the town plainly does exactly that: around 700 planning applications were lodged across the area in the past year, which is the sound of a place busily extending, converting and building rather than sitting frozen in aspic. What you will not run into, for a standard unlisted house, is a conservation-area layer insisting you match the original brick or keep the original windows down to the last hinge.
The verdict is generous by most towns' standards: your freedom to extend or alter a home in Patchway runs high. Confirm your own property is not one of the couple of dozen listed exceptions, measure your plans against the permitted-development limits or apply if they go beyond, and past that the town largely lets you get on with it. For a buyer who wants a house they can change rather than a relic they have to preserve, that is close to the best answer a place can give.