Are goods and services supplied to a qualifying educational institution ever not zero-rated?

Yes, there are supplies related to providing educational services which are subject to the standard VAT rate of 5%. A qualifying educational institution must charge and account for VAT for the following supplies:

• Goods and services supplied by a qualifying educational institution to persons who are not enrolled in the institution.
• Any goods other than educational materials that are provided by a qualifying educational institution and consumed or transformed by the students being taught. 
• Uniforms or any other clothing which are required to be worn by students at a qualifying educational institution, irrespective of whether they are supplied by the institution as part of the supply of educational services. 
• Electronic devices used in educational services, irrespective of whether they are supplied by a qualifying educational institution as part of the supply of educational services.
• Food and beverages supplied at a qualifying educational institution, including supplies from vending machines or vouchers for food and beverages.
• Field trips, unless they are directly related to the curriculum of an educational service and are not predominantly recreational.
• Extracurricular activities provided by or through a qualifying educational institution for a fee in addition to the fee for the education service.
• Membership in a student organisation. 

Another exception to zero rating is the provision of school transportation, which falls under the category of domestic transportation and hence is exempt from VAT.