England such as it was was clear of schools before St August inexorably from which there is a straight line of ecclesiastical involvement until comparatively recently.
Secular provision as we know know is not a fixed priority.
The level of ignorance is stunning.
What about the provision of schools by the Romans from AD43 to about AD400, which predates St Augustine by hundreds of years.
And, of course, the education and schooling established under the Roman model was much more recognisable in a modern context, in that it was broadly educational, covering a range of subjects, from writing to maths to rhetoric. It wasn't specifically linked to a single vocation and wasn't basically vocational training. The 'education' established by St Augistine and thereafter wasn't education as we know it, it was training for the clergy. There is a difference between education and training.
Indeed broad educational provision (broad in content of course, rather than broad in who benefited) effectively vanished for hundreds of years following the end of the Roman period, really only reappearing in the 12th and 13thC when a series of new schools remerged whose remit was not purely the vocational training of clergy, but broader education for the local community (albeit only those from wealthy backgrounds). While some of those schools were re-purposed cathedral schools, many others were foundations of the civic society of the town or city in which they arose. Indeed quite a few are still in existence.
But the basic point is that the earliest formal educational and schooling in this country predates the arrival of christianity at it was Roman - and the Roman educational model was secular and civic, not religious.