The IR35 legislation specifically challenges those people who supply their services to clients via their own company, often known as a 'personal service company', or a limited liability partnership, who, in the  eyes of the HMRC, should be classed as 'disguised employees'.
IR35 only applies to staff not paying PAYE directly on their earnings so anyone paid through the school payroll is not affected.  Contractors paid through an umbrella company are also not affected as the umbrella company deducts PAYE in the usual way from the staff using them.
If you want to check the employment status of a contractor paid on receipt of invoices use this link
 https://www.gov.uk/guidance/check-employment-status-for-tax

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