Gov.uk state that “an employer doesn’t usually have to give a work reference - but if they do, it must be fair and accurate. Workers may be able to challenge a reference they think is unfair or misleading”.
Normally, employees would have the right under the General Data Protection Regulations (GDPR) to access information about themselves that an organisation has stored. However, there is an exemption under schedule 2 to the Data Protection Act 2018 (which supplements the GDPR) that allows any organisation to decline to disclose a confidential employment reference to an employee or former employee if they request to have access to it.
An employer that is covered by the exemption can still choose to provide the employee or ex-employee access to the reference. The employer should be careful not to disclose information about a third party involved with the reference. For example, the person who wrote it.