Yes, and heritage is unlikely to be what stops you. There is one listed building. There are no conservation areas. The neighbours lodge planning applications at a steady clip. The thing worth worrying about is under the lawn, not in the council's heritage file.
Historic England's list records one listed building in Whitehill, and it is Grade II. There are no Grade I or Grade II* buildings at all. Listing means any change to that building, inside or out, needs listed building consent on top of any planning permission, and the rules are strict enough that owners of listed homes learn the name of the conservation officer before the name of the postman. With a single listed building in the whole area, the odds of buying it by accident are slim, and the odds of your extension being judged against its setting are low for almost every other street. No conservation areas cover Whitehill either, so there is no extra layer of control on windows, roofs, front walls or demolition for the ordinary house.
The surrounding land holds four scheduled monuments, the strictest protection tier in England. They matter to anyone with a plot next to one, where ground disturbance can need separate consent, and to nobody else extending a semi.
The appetite for building work is plain in the planning register. Between March 2024 and June 2026, 594 planning applications were lodged for the area, 262 of them in the last twelve months. That is a place where people extend, convert and alter homes as a matter of routine, and where the neighbours' own kitchen extensions are the most useful precedent a buyer can study. How many of those were approved is not something this page can say, so look up the decisions on specific applications near any house of interest.
The real constraint is the ground. The British Geological Survey rates shrink-swell risk at class 3 across every postcode in Whitehill, 100% of them. Shrink-swell ground expands when wet and contracts when dry, which moves foundations over the seasons and is the classic cause of cracks in extensions that were built as if the soil were rock. It does not stop anyone extending. It does mean deeper or more carefully designed foundations, attention to nearby trees and drainage, and a structural engineer's view before the builder's quote is accepted. The builder who says the ground is fine without looking at it is quoting for the easy version of the job.
In practice, many single-storey rear extensions, loft conversions and outbuildings on ordinary houses can go ahead under permitted development rights, without a full planning application, provided they stay within the national size and position limits. With no conservation area and almost no listed buildings, those rights apply to most Whitehill homes in full. Anything bigger, a second storey or a change that breaks those limits, needs planning permission from East Hampshire, and a lawful development certificate is a cheap way to confirm that a permitted project really is permitted before the diggers arrive. Building regulations apply either way, which is where the foundation question gets answered properly.
Freedom to extend is one of Whitehill's real advantages: the planning paperwork stays light and the heritage rules barely touch most homes. The ground asks for a better foundation, not a better argument with the council.