Mostly yes, unless you bought one of the old ones. There are no conservation areas to tiptoe around. There are a few dozen listed buildings, and they carry most of the restrictions. The neighbours file hundreds of planning applications a year. In Buxted the question is rarely "can I" and usually "which house did I buy".
The Buxted area has 79 listed buildings. One is listed at Grade I, 6 at Grade II* and 72 at Grade II. Listing covers the whole building, inside and out, so changes that affect its character need listed building consent on top of any planning permission. That reaches past extensions to windows, doors, internal walls and the fireplace the previous owner boarded up. For the 72 Grade II homes and buildings the process is well trodden and routine. For the handful graded higher, expect the conversation to be longer and the answer more often "not like that". Buy a listed house for its character and you've also bought a partner in every future decision about it.
There are 4 scheduled monuments in the area, the strictest tier of protection going. They matter mainly if your land sits next to one, and if it does, your solicitor should raise it before you've picked a spot for the garden room.
Nobody is short of plans. The planning records covering the area show 2,034 applications between April 2024 and June 2026, and 839 in the last twelve months alone. That doesn't say how many got through, and nothing here should be read as an approval rate. It does say that altering homes around Buxted is normal, not a heroic battle with the council. The loft conversions are coming whether you're ready or not.
For most houses the practical picture is simple. With no conservation areas in the area, an unlisted home follows the ordinary national rules, and many modest extensions fall under permitted development without a full application. Parts of the area sit inside the High Weald Area of Outstanding Natural Beauty, though, so check whether a house falls inside it before assuming the standard allowances apply. Check the listing status of the exact address, read the title for past conditions that might remove permitted development rights, and ask the vendor for the paperwork on any extension already built. An unrecorded conservatory is a problem you inherit at the price of the house.
Your freedom to extend in Buxted is fair to middling: easy on most of the post-war and modern stock, harder on the listed minority. Pick the house with the plans in mind, not the other way round.