Yes, but in the old town you'll need permission for more than you'd expect. Hundreds of buildings are listed. Nine sites carry the strictest protection there is. The neighbours file hundreds of planning applications a year anyway. Extending in Sandwich is possible. Doing it quickly and quietly usually isn't.
The listing count is the story here. The area holds 441 listed buildings: seven at Grade I, 26 at Grade II* and 408 at Grade II. Listing covers the whole building, inside and out, not only the front people photograph, so an extension, a new window, a removed wall or a replacement staircase can all need listed building consent on top of any planning permission. Grade II covers most of them and still means the council's conservation officer gets a say over your kitchen. Grade II* and Grade I buildings face closer scrutiny again. Carrying out works without consent is a criminal offence, not a planning technicality, and the surveyor asking "was this done with consent" is asking for a reason.
The area also has nine scheduled monuments, including long sections of the town walls and a Saxon Shore fort and Roman port at Richborough. Scheduling is the strictest protection tier and mostly matters for land on or right next to one, where even digging a foundation or laying a drain needs separate consent. For a house backing onto a stretch of wall, the monument decides where the extension can go.
None of this has stopped anyone trying. The planning register shows 625 applications between April 2024 and June 2026, 263 of them in the most recent twelve months. That's plenty of households wanting a bigger kitchen, and plenty of paperwork to go with it. The volume shows people here do alter their homes. It says nothing about how many got what they asked for, so look up the decisions on your own street before assuming your plans will pass.
Mining is a minor factor but worth a line. The whole area falls inside the coalfield consultation zone, about 1% of postcodes have a recorded mine working within 500 metres, and none sit directly over one. The nearest recorded working is about 460 metres from the closest postcode. In practice that means a mining search as part of conveyancing, and possibly a specialist report if one comes back flagged, which a lender or insurer may ask to see. It isn't a prediction that anything will move.
In practice, a house that isn't listed and isn't next to a scheduled monument will usually have the ordinary permitted development rights that let modest extensions go ahead without a full planning application. A listed house doesn't escape consent that way: work affecting its character needs listed building consent whatever its size. Before offering on an older property, check the listing entry, ask the council what permitted development rights the house still has, and budget time for consent as well as money for builders. Buyers who assume a rear extension is a formality tend to learn otherwise just after completion.
Your freedom to extend here is limited, especially in the older core, where the paperwork often takes longer than the building work. Outside the listed streets it's ordinary. Inside them, expect to ask permission for most things.