The schools in Whiteley are a local primary inside the town plus a second primary, with secondary-age children travelling out to schools in the surrounding villages and towns. Whiteley Primary School is the original. A newer primary opened more recently. The secondaries serving the wider area include The Hamble School, Brookfield Community School and Henry Cort Community College. The official grading information for any of these is not in the brief this answer draws from, so what follows is the structural picture rather than the league-table picture.
Hampshire's school-allocation system runs on distance and on sibling priority, so a named school in your area does not guarantee a place at it. The popular schools fill up before the catchment edges do, and the catchment edges move every year. Whiteley has been a growing settlement for two decades, with a further phase approved at North Whiteley that will bring more school capacity once it opens, including additional primaries and another secondary. Until then, demand for places at the existing schools is rising faster than supply, and the admissions distance a successful applicant has to live within has been creeping in, not out. About three in ten households here are couples with children and the typical resident is in their late thirties, which keeps the school question live across most of the town. Anyone buying here for a specific school should check the current admissions distance for the year their child applies, not what a friend-of-a-friend got five years ago. The map moves when the houses do.
So, the schools in Whiteley are typical Hampshire commuter-town schools, with the upside that the primaries are inside the town and the downside that the secondaries are not. Anyone making a buying decision on schools needs to read the current admissions data for the specific school, not the reputation of the postcode.