Yes, and with less red tape than most of Hampshire throws at you. The entire area carries only five listed buildings, every one of them the lowest grade. There is no conservation area drawn across the streets and no scheduled monument to design around. The housing stock is mostly modern, which means the heritage machinery that slows older towns to a crawl barely turns here. If your plan is a rear extension or a loft conversion, the constraints are the ordinary national ones, not an extra local layer sitting on top.
Put the listings in perspective. Five protected buildings across a whole town is close to nothing, and all five sit in grade two, the most common and least restrictive tier of listing. If you happen to own one of them, the rules do bite: you need listed building consent for alterations inside and out, and a conservation eye falls on materials and detail in a way it never does for an ordinary house. But the chance of that applying to you is slim. The overwhelming majority of homes here are unlisted and, as far as the planning system is concerned, gloriously unremarkable, which is exactly the status you want when you are trying to add a bedroom rather than preserve a monument.
For that typical unlisted house, a good deal of everyday work falls under permitted development, the national rights that allow certain extensions and loft conversions without a full application. Those rights are not unlimited and they can be stripped back on some newer estates and for some property types, so the sensible move is always to confirm what applies to your specific address before anyone lifts a spade. Anything past those rights goes in as a householder planning application, and the local authority is visibly practised at handling them. The area has processed well over a thousand planning applications in the past couple of years, with hundreds in the last twelve months alone. This is a planning office that deals with people extending houses as its daily bread, not one that treats every request as a novelty.
The verdict is a four out of five for freedom to build. Unless you have bought one of the five listed buildings, the only things standing between you and a bigger kitchen are your budget and the national rulebook that applies everywhere. If you want a town thick with heritage character, look somewhere older. If you want a town where you can get on with the work, this is about as unobstructed as it gets.