Yes, for most houses in Edenbridge extending is a routine planning job. The timber-framed old buildings are the exception, not the rule. No conservation area is recorded across the town. The neighbours send in plans all the time. Buy a post-war semi and you can extend it. Buy one of the timber-framed ones and you'll mostly be looking after it.
Edenbridge has 48 listed buildings: one Grade I, four Grade II* and 43 Grade II. Listing covers the whole building, inside and out, so changes that alter its character need listed building consent, on top of any planning permission. That can include new windows, a knocked-through wall or an extension on the back. Most of these buildings belong to the medieval core and the farmhouses around it, so the rules touch a small corner of the town's housing. Anyone buying one should expect every alteration to be a careful conversation with the council.
The area also has one scheduled monument, the strictest tier of protection, which mainly matters if you own land close to it.
Your neighbours are not frozen in place. The planning register holds 874 applications between April 2024 and June 2026, and 376 of them came in the most recent twelve months. That's a town still adding kitchens, loft rooms and garden offices. The planning portal is no stranger here.
For an unlisted house outside a conservation area, many modest changes can go ahead under permitted development without a full planning application. Rear extensions within size limits, some loft conversions and outbuildings are common examples. The rules have limits and conditions, and a house on a newer estate can have those rights removed by its original planning consent. Check with the council before a builder gets out the digger. For a listed building, assume everything needs consent until the council tells you otherwise.
Edenbridge is middling for freedom to extend. Most of the town's housing can be enlarged with ordinary paperwork. The listed buildings are where the tight control is, and there are just enough of them that buyers should check the listing register before they plan the extension.