Most, or almost all schools in this time period were religious with the main goal of studying religious texts
Either that or they were established to teach Latin grammar also with the purpose of nurturing sons of the aristocracy destined for priesthood or monastic work
Two universities were established in affiliation with the church: the University of Oxford, followed by the University of Cambridge, to assist in the further training of the Catholic Christian clergy.
Augustine of Canterbury, a monk and one of the founders of the English Church, established a church in Canterbury in 597, which included a school for the study of religious texts.
This was joined by another school in year 604 at what is now Rochester Cathedral. Further schools were established throughout the British Isles in the seventh and eighth centuries, usually to just teach Latin or train singers for Cathedral Choirs