Yes, but the village gets a say in how. Nearly a hundred buildings here are listed. Two conservation areas cover the historic core. The whole parish sits inside protected countryside. Extending in Mayfield is possible, but it isn't a weekend job.
Historic England lists 92 buildings in and around Mayfield: 3 at Grade I, 3 at Grade II* and 86 at Grade II. Listing covers the whole building, inside and out, so any alteration that affects its character needs listed building consent on top of any planning permission. That means a new window, a knocked-through wall or a replacement staircase, not only an extension. Doing the work first and asking afterwards is a criminal offence for listed buildings, not a paperwork slip. If the house you like is listed, the survey and the heritage conversation should both happen before the offer.
There are 2 conservation areas around the village, Mayfield and Coggins Mill. Inside them, demolition and some external changes need consent that an ordinary street would not, and the council judges new work on whether it preserves the character of the area. The same street frontage that sold the house to you is the thing the planners are there to protect. Buyers who fall for the old high street and then plan a glass box on the front have misread which part they are paying for.
The whole parish also lies inside the High Weald Area of Outstanding Natural Beauty. In protected landscapes like this, the national permitted development rights are narrower than elsewhere, so some extensions that would go ahead without an application in an ordinary suburb need full planning permission here. Rear-garden projects that are routine in town can turn into a formal application.
The neighbours are not deterred. Wealden's planning records show 262 applications in the Mayfield area between April 2024 and June 2026, 114 of them in the last twelve months. That is a village that keeps extending, converting and replacing things, just with forms filled in first. The applications list is also the quickest way to see what the house next door has in mind.
In practice, check three things before buying with an extension in mind. Find out whether the house is listed, whether it falls inside a conservation area, and which of the usual permitted development rights still apply in the High Weald. An unlisted house outside the conservation areas, with space at the back, is the easiest case. A listed cottage on the high street is the hardest, and the price should reflect it.
Your freedom to extend in Mayfield is middling. Plenty of neighbours do it, but on the council's schedule and within the village's rules, not on their own terms.