Mostly yes, with three large asterisks. The area carries 113 listed buildings. Four conservation areas pull boundaries across parts of both villages. About a quarter of the postcodes sit inside an Area of Outstanding Natural Beauty. Your freedom to extend depends almost entirely on which side of those lines your house happens to sit.
The 113 listed buildings break down into three at Grade I, four at Grade II star, and 106 at Grade II. Anything inside that list needs listed building consent for almost any alteration that touches the historic fabric, which in practice covers windows, doors, internal walls, roof finishes, and most of what makes a house feel like a different house when the work is finished. Grade I and Grade II star carry the stricter end of the regime, with Cakeham Manor at the head of the local list as the kind of property where the consent process and the building work proceed in parallel for the lifetime of the project. The 106 Grade II properties are the great majority of the local listed stock, and the rules there are more workable but still rule out the lazier kinds of refurbishment. If you are buying any listed property, the consent process is a project of its own running alongside the build, with its own timetable and its own appeals.
Four conservation areas cover Somerley, Earnley, West Wittering and West Itchenor. Inside any of these, the trees are protected by default, demolition needs separate consent, and the local authority can place tighter limits on alterations to street-facing elevations than the national permitted-development regime would otherwise allow. There is also one scheduled monument in the wider area, which removes ground-disturbance freedom entirely from the affected site. The names matter when buying. A property on a postcode close to a conservation boundary may or may not be inside it, and the boundary maps are the only authority worth trusting on which side a particular front door sits.
In practice, the bulk of the housing stock sits outside both the listed register and the four conservation areas. For those houses, the standard permitted-development rights apply, and a single-storey rear extension or a loft conversion can usually proceed without a full planning application. The number of planning applications submitted across the wider area over the last twelve months ran to about 610, which is the volume the local planning office is currently processing, much of it routine domestic work on the post-war stock. Anything more ambitious, such as a second storey or a substantial change to a frontage, usually still needs consent regardless of conservation status, simply because of scale. The planning office here is not unfriendly. It is just busy, and the appeals system exists for the cases that need it.
Average. Most homes here can be extended on the standard rules, but the heritage layers carve out a meaningful minority where every change is paperwork.