JPAG Section 4 page 24/25 is a more current and comprehensive reference:
https://www.nalc.gov.uk/library/our-work/jpag/3859-practitioners-guide-2023/file
Independence
4.9. Independence requires the absence of any actual or perceived conflict of interest. It means that whoever carries out the internal audit role does not have any involvement in, or responsibility for, the financial decision making, management or control of the authority, or for the authority’s financial controls and procedures.
4.10. A current or recent authority member, who cannot demonstrate independence from decisions in the year to be audited, cannot be its internal auditor. Similarly, it would not be appropriate for any individual or firm with a personal connection to a member or officer of the authority to be appointed. Conflicts of interest must be avoided, such as in cases where an external provider of accounting software or services to the authority, also offers internal audit services through an associate company, firm or individual.
4.11. There is no requirement to rotate auditors but the independence of the appointed person or firm should be reviewed every year with regard to; personal independence, financial independence, and professional independence.