Good, and boringly so, which is the best thing schools can be. One secondary serves the whole town. Two primaries split it north and south. The Ofsted picture across the county is strong enough that the interesting question here is not quality but capacity. Nobody moves to Bradford-on-Avon for the schools, and nobody has to move away because of them either.
Across Wiltshire, Ofsted has graded 128 settings and rated 106 of them good or better, which is a little over four in five. Six hold outstanding. Twenty require improvement and two are rated inadequate, so the county is not uniformly excellent, but the weight of it sits firmly on the good side. A further 73 settings hold no published grade at all, either because they have not been inspected under the current framework or because their inspection is not yet published, and those are simply unknown rather than bad.
Those counts describe the whole local authority, not this town. Wiltshire is a large and mostly rural county, and an average built from Salisbury to Swindon's edges tells you about the system rather than about the two primaries on your walk to work. Look up the individual reports before you commit to anything.
St Laurence School is the secondary, formed in 1980 out of a merger of the town's grammar and secondary modern schools, and it also hosts the Wiltshire Music Centre on its grounds, which is a genuinely unusual thing for a town this size to have attached to its comprehensive. The archaeology on its playing fields turned up a Roman villa with a well-preserved mosaic, so the school sits on the oldest piece of settlement in the town. For primaries, Christ Church Church of England Controlled Primary School serves the north and Fitzmaurice Primary School the south, the latter opened in 1928. Beyond the town boundary, Westwood-with-Iford and Winsley are the nearest alternatives, both small village primaries of the kind that fill from their own lanes first.
Which brings up the thing estate agents will not put in the listing. Naming a school is not the same as getting into it, and Wiltshire allocates places on its own criteria rather than on which street you liked the look of. A single secondary serving a town of this size means the question is not usually which school but whether there is room, and that answer changes year to year. Anyone buying on the assumption that proximity equals admission is making a decision on a hope rather than a rule.
The schools are one of the genuinely strong things about this town, which is a rare sentence to be able to write about anywhere with this much heritage protection and this little space. The buildings may be listed and the parking may be a nightmare, but the education is not the thing you will be complaining about.