The Education (Pupil Information) (England) Regulations 2005 (EPIER) give any person who has parental responsibility for a child, or who has care of them, access to the educational record of the child.
The specific meaning of "educational record" is set out in the Regulations. Full details of the Regulations can be found here.
The main differences between these regulations and the DPA are that parents accessing their child's personal data under the DPA are in fact exercising the child's right of subject access on their behalf, and a sufficiently mature child has the right to object to this. The pupil cannot prevent a parent from accessing their educational record under EPIER. Not all of a pupil's personal data held by a school are contained in their educational record, such as notes made by teachers for their own use, or information provided by the parent of another child. Therefore the scope of a DPA subject access response would be wider than an EPIER response.