Jill was very anti private education, but Phil wasn't. Shula and Kenton went to Borchester Grammar School, which was a state school, but David and Elizabeth were sent to fee-paying boarding schools. Before my time as a listener, but I suspect that David didn't pass the 11+ and by the time Elizabeth was old enough possibly the 11+ had gone and Phil was too snobbish to contemplate a comp for his youngest.
John, Helen and Tom all went to Borchester Green, which is a co-ed comp and as far as we know the only state secondary school for miles around, and so did Pip, Josh and Ben. Pip was going to take the entrance exam for the Cathedral School in the hope of getting a music scholarship, but it was a last-minute decision necessitating intensive tutoring and extra music practice and she really wasn't up to it, so didn't do it in the end. John went to a state boarding school latterly because of its agricultural specialism (I didn't imagine this, did I? Peggy paid for the boarding element.)
Lily and Freddie went to the Cathedral School (academically selective fee-paying day school) as a compromise because Nigel wanted them to go to boarding school and Elizabeth couldn't face that. They did go to Loxley Barratt first.
Daniel went to the Cathedral School after LB too. Alice went to St Margaret's, a private girls' day school, probably from age 4/5, and then insisted on going to Borchester College for sixth form. Kate and Debbie went to fee-paying boarding schools and so did Adam (and now Ruairi too, of course).
All the non-Archer children go to LB and then Borchester Green and, if they stay in education that far, on to Borchester College.