Yes, most homes in Clutton can be extended, so long as yours is not one of the listed ones. The wider area carries around 80 listed buildings, none of them top grade. A single conservation area sits within the surrounding patch, over at Timsbury. The great majority of the village housing carries no special protection at all. Extend an ordinary house here and the council is a hurdle, not a wall.
Listing is the thing that changes the game. Around 80 buildings across the area hold listed status, and the good news for most owners is what that number does not contain: not a single one is in the highest grade, the kind that all but freezes a building in place. Five carry the middle grade, the ones flagged as more than merely of special interest, and the remaining seventy-odd sit in the standard grade that covers the bulk of protected homes. If your house is listed, even at that standard grade, you need consent for changes an unprotected house would not, inside as well as out, right down to the windows and the internal walls. If it is not listed, and most Clutton homes are not, none of that lands on you.
Conservation areas add a second layer, and here there is only one of them to reckon with, at Timsbury within the surrounding area. Inside a conservation area the ordinary freedoms shrink: some work that would be automatic elsewhere needs the council's blessing first, trees pick up protection, and the character of the street becomes something you are expected to keep rather than reinvent. The point worth holding onto is that this covers one defined patch, not the whole of Clutton. Most addresses fall outside it and keep their normal rights.
For the typical unlisted house sitting outside that conservation area, the practical answer is that a good deal is possible without a full planning battle. Permitted development rights already cover many of the standard moves, a rear extension or a loft conversion, before you ever need to formally apply. Where owners do apply, the local system is plainly in working order: around 25 planning applications went in across the area in the past year, with none withdrawn, which is the mark of a place where sensible schemes get through rather than one where everything ends in a fight. The real variable is your specific property, not the village as a whole.
So can you extend a house in Clutton? For most houses, yes, with the usual paperwork and a bit of common sense. Freedom to alter sits middle of the road here: wide open if your home is ordinary, genuinely restricted if it happens to be one of the listed few or inside the conservation area. Check the listing and the map before you buy the ladder.