Yes, with almost nothing standing in the way. Two listed buildings in the area, both Grade II. No conservation areas inside the village footprint. No scheduled monuments. The local heritage layer adds no constraint on top of the standard national rules, which is the buyer's freedom in practice.
The listed-building count for the area is two, both at the lower Grade II tier. None are Grade I, none are Grade II-starred. Listing means the building's external appearance, character and significant internal features are protected: you cannot replace the windows, knock through a load-bearing wall or extend the footprint without listed-building consent, and that consent process is genuinely demanding. If you happen to be buying one of those two listed properties, the rules apply in the usual way and the right move is to read the listing description for the building before you put an offer in. If you are buying anything else in the village, listed-building rules are simply not a concern.
The conservation-area picture is the other half of the heritage question, and that picture is blank. There is no conservation area drawn over the village itself. There are conservation areas in nearby places, including Catherington, Horndean and the Sir George Staunton Country Park to the south, but none of them reach into Cowplain. The scheduled-monument count inside the village footprint is also zero. The protected archaeology and the protected streetscapes both sit on someone else's map.
With no local heritage overlay, the normal national framework for permitted development applies in full. Loft conversions, single-storey rear extensions, side returns, garden rooms, replacement windows, solar panels and off-road parking conversions are mostly achievable without a full planning application, subject to the standard size, height and proximity rules that apply across England. Two-storey extensions, larger alterations, anything affecting a shared boundary, and anything tipping over the permitted-development thresholds still go through the planning system in the normal way. The local planning authority has been processing somewhere around 685 applications across the wider area in the past twelve months, so the system is well used to handling resident extensions and the timetable is what it usually is for a Hampshire borough.
Two practical caveats are worth naming. First, the post-war semi-detached and terraced stock that dominates the village shares party walls, which means any internal works affecting the shared structure trigger the standard party-wall agreement process, and that is a neighbour-consent matter rather than a planning one. Second, the village has very little pre-1930 stock, only about 2 percent of homes, so the kind of period-property planning judgements that make older areas slow do not really feature here. The buyer extending a 1960s semi is dealing with the same rules anyone in suburban England deals with, no more.
The verdict on freedom to extend or alter is excellent, scoring five out of five on the heritage constraints. A post-war village with two Grade II listings, no conservation areas and no scheduled monuments is about as unconstrained as English planning gets. The neighbours, the boundary lines and the local planning authority's published policies still apply. The heritage system does not.