You can extend a house in Swanmore, but you should assume the area will have something to say about how. This is heavily listed, heritage-thick countryside. Over four hundred protected buildings sit across the wider area. Seven separate conservation areas cover a good deal of the map. None of that makes an extension impossible, but it does mean the answer more often starts with a planning officer than with a builder.
Listed buildings are the strictest end of it, and there are a lot of them here. The wider area carries over 400 in total, the overwhelming majority at the standard grade, with around twenty at the middle grade and a handful at the very top. If the house you are eyeing is one of them, the ordinary permitted-development freedoms effectively vanish, and almost any meaningful change, inside or out, needs listed-building consent before a single wall moves. That covers the things people forget count as alterations, from windows to internal layout to what you do with a chimney. Buying a listed house because it is beautiful and then resenting the rules that kept it beautiful is a well-worn local mistake, and the paperwork does not care that you fell in love with it.
Conservation areas widen the net beyond the listed few. Seven of them sit across the area, and being inside one tightens the rules even for houses that carry no listing of their own. Conservation status can pull back some of the permitted-development rights a homeowner elsewhere would take for granted, so changes to the frontage, the roofline, and sometimes even the trees can need consent that would be automatic a few miles away. The point of the designation is to keep the street looking as it does, which is lovely to live in and less lovely when you want a modern box on the back.
In practice, the honest advice is to check before you commit rather than after. Some homes here still carry ordinary permitted-development rights and a straightforward rear extension will go through with little fuss. Others sit under enough protection that even modest work becomes a consent application with drawings, fees, and a wait. The only way to know which camp your specific house falls into is to look up its listing status and its conservation position for that exact address, and to do it before you have already priced the loft conversion in your head. The village is old enough that assumptions are expensive.
So can you extend a house in Swanmore. Sometimes freely, often only with permission, and the area sits firmly on the restrictive side of the scale. Come with realistic plans and professional advice and plenty gets built here. Come expecting to do as you please with an old house in a protected village and the answer will be a long and patient no.