Yes, and people do it constantly, but the answer depends entirely on which side of a boundary line your house sits on. Two hundred and sixty-odd buildings here are listed. Three conservation areas cover the older parts of town. Hundreds of applications go in every year regardless. Bideford is not a town where you cannot build. It is a town where a fair number of owners find out the rules after they have already chosen the windows.
Historic England's register carries 263 listed buildings in and around Bideford: 2 at grade one, 11 at grade two star, and 250 at grade two. Listing applies to the whole building, inside and out, and to anything fixed to it. Replacing windows, opening up a chimney breast, adding a rear extension or fitting solar panels all move from a decision you make into an application you submit, and listed building consent is a separate process from planning permission rather than a box within it. Work done without it is a criminal offence rather than a paperwork problem, which is the detail that tends to surprise people who bought a period house because they liked the fireplaces.
Three conservation areas sit over the town: Bideford, Bideford East, and Bideford at Clovelly Road. Conservation area status does not freeze a house, but it narrows what you can do without asking. Demolition, tree works and some alterations that would be permitted development elsewhere require consent inside the boundary, and the council assesses proposals against whether they preserve or enhance the character of the area, which is a standard that is easier to fail with uPVC than with anything else on the market. The boundaries do not follow tidy lines, so the only reliable check is the address rather than the street.
There are also 2 scheduled monuments recorded in the area. That is the strictest protection tier in the system and it applies to the monument and its setting rather than to ordinary housing, so for most buyers it matters only if the land you are eyeing sits close to one.
The volume of activity says the rest. Torridge District Council's planning register logged 1,309 applications across the area between April 2024 and June 2026, with 565 of those in the most recent twelve months. Whatever the constraints look like on paper, this is not a town where nothing gets built. People extend, convert, reroof and rebuild here in numbers.
Practically, that leaves two versions of the same question. Outside the designated areas, with an unlisted house, the usual permitted development rights apply and a rear extension or a loft conversion is often a matter of confirming rather than applying. Inside a conservation area, or in a listed building, assume consent is needed and price the professional fees in before you offer, because the cost difference between the two versions of Bideford is real and it lands on the buyer, not the seller.
Freedom to alter a home here is below what most towns of this size offer, and the reason is simply how much of the old town is protected. Check the listing and the conservation area boundary on the specific address first. Everything else about the project follows from that one answer.