Almost certainly, because very little here is protected enough to stop you. Only a few dozen buildings are listed. None is in the top grade. No conservation area is mapped. Your neighbours lodged nearly a thousand planning applications last year. If your extension gets stopped, it will more likely be by a neighbour than by a heritage rule.
Southborough has 36 listed buildings: 35 at Grade II, 1 at Grade II* and none at Grade I. Listing covers the whole building, inside and out, so changes to a listed home need listed building consent as well as any planning permission, and a conservation officer will read your plans closely. For a town of this size, 36 is a small share of the housing stock. Unless your house is one of them, listing is somebody else's problem, and the estate agent's particulars will say if it isn't.
Plenty of people here are building. Planning records show 2,097 applications between April 2024 and June 2026, including 945 in the most recent twelve months. That total covers everything from loft conversions to garden rooms, and it doesn't say how many were approved. What it does say is that altering a house here is ordinary, not a fight.
In practice, most Southborough homes are ordinary houses that are neither listed nor inside a conservation area. That is the starting point for permitted development, which lets some smaller extensions and alterations go ahead without a full planning application, within national size and design limits. Anything bigger, anything on a listed building, and anything on a flat needs consent. Before you draw anything, check the address with Tunbridge Wells Borough Council and ask for a lawful development certificate if you want written confirmation that a project doesn't need planning permission. It costs less than a legal argument with the neighbour's solicitor.
For anyone wanting to build, Southborough is one of the easier places in the borough, because very little is protected and a lot is already being built. Plans are more likely to be slowed by the neighbours than by the heritage rules.