I have been fortunate to live in places in England where my kids just went to the nearest school (or the one in whose catchment area they lived in if they were near a catchment border), as I and my siblings did when we went to school.
The same in Scotland. When DH was house-hunting in Scotland and I wasn't because I was still in England, my main requirement other than it be livable in was that the primary school, which we could assume Minibags would get a place in, should be within walking distance – just over a mile as it happened and she managed fine from five and a half.