I find myself somewhere in between Jules and Mentorman on this point.
A person appointed as an 'office' holder (RFO, PO in this example) for an organisation cannot be self employed according to current guidance.
But if, as is indicated in the OP, the locum is simply providing secretarial services, and they satisfy all of the other requirements of self employment status, then perhaps they 'could' be self employed - if that is what the council are content with. If it is, then the (self employed) employee should b invited to supply their HMRC UTR and that would satisfy due diligence that the council had taken reasonable steps to ensure correct SE status. There is also an HMRC employment status assessment tool which helps in this regard.
Either way, the point is that the EMPLOYER dictates the terms of the employment NOT the employee.
Life would be a goof deal simpler - and efficiency a great deal better - if clerks were all SE and paid according to performance.