I believe I am right in claiming that this building in Ewelme is the oldest to be used as a school in the State system (i.e. not Private Sector).
Dating from c.1437* in the reign of the Plantagenet King Henry VI (over 50 years before the birth of Henry VIII) it is still being used for its original purpose nearly 600 years later.
It is the south-westernmost of a remarkable group of Grade I listed buildings, comprising the church, almshouses, this school and various other listed outbuildings and walls.
A county primary school, its website
Link states that it is "a Church of England Voluntary Aided Primary School founded in 1437 for the education of any child."
There are some lovely and intriguing old features to this building such as
SU6491 : Windows of Ewelme CP school
It is Grade I listed
Link and the wall seen to its right in this photo is separately Grade II listed
Link
See also
SU6491 : Ewelme County Primary School
*Note: The EH listing gives a date of c.1450, but the school's own website states the slightly earlier date of 1437.