North Baddesley teaches its own primary-age children and sends the teenagers out. The village has both an infant school and a junior school inside its boundaries, so the early years are covered on the doorstep. There's no secondary school in the village itself, which means the older children travel out, roughly ten minutes away by car to the nearest one. What the village doesn't have is a current inspection grade on record for any of it. That gap matters more than a house-sale brochure would ever admit.
The two schools are North Baddesley Infant School and North Baddesley Junior School, which between them carry a child from starting age up to the move to secondary without leaving the village. The infant school is the older institution of the two, teaching the village's youngest since 1876 and running specifically as an infant school since 1969, which is a long run of small children going through the same front gate. For a village of this size, having the infant and junior stages split into two dedicated schools rather than crammed into one is a genuine point in its favour, whatever the inspectors would or wouldn't say about them.
Two things are worth being blunt about before anyone buys a house on the strength of the local schools. The first is the catchment trap. Living near a named school is not the same as being handed a place in it. Proximity gets you into the conversation, not through the door, and admission rounds have a habit of being honest with people who assumed the house three streets from the gate was a guarantee. The second is the missing grade. With no current published inspection rating for the village schools, the reputation you hear on the school run is exactly that, a reputation, not a verdict. Don't treat playground consensus as an inspection report. Pull the latest report yourself, read it properly, and decide on the evidence rather than on the postcode.
None of the village schools have closed or merged recently, so the two names are the two names, and the setup is stable rather than shifting under your feet. That stability is worth something in itself. Plenty of buyers have chased a school only to find it swallowed by a reorganisation the year after they moved.
The honest verdict is that North Baddesley's schools are an unknown quantity wearing the costume of a safe bet. Two dedicated village schools on the doorstep, a short drive to secondary, and no grade on the books to prove any of it is brilliant or otherwise. Average until you've done the reading, and this is a question that rewards doing your own homework rather than trusting the view from the street.