A small beautiful (state) primary in Suffolk I remember is the one in Lavenham, such a lovely village. Close enough to Bury St Edmunds.
Flip side being housing is a bit pricey (of course). In the UK it is a really a case of small, good state school = expensive neighbourhood.
I second Devon. Tavistock another favourite of mine. Close to Plymouth for shopping.
I don't like Cambridgeshire- I hated the commute down the A14- super congested, always accidents and loads of speed cameras. However Kimbolton is lovely and if you don't mind using the train you can drive to Peterborough and catch the fast train to London. Or if you like a taste of village en route to London, I would suggest Buckden. Small but with top quality shops.
For my money though, I would say how about beautiful Harrogate? I loved Knaresborough. When we lived in Yorkshire, we though of moving there before deciding to emigrate altogether.
Some ideas there- hope it helps?