According to data protection legislation, anytime an organization processes personal information, they should explain the lawful basis for doing so. The Oral History Society provides excellent advice on this subject. This is what they say about what lawful basis to use for the collection of oral history recordings.
OHS advice therefore (drawing on British Library policy) is that for the processing of personal data for archival purposes a data controller should normally rely on the legal basis of ‘the performance of a task carried out in the public interest’ where legally able to do so, or on ‘legitimate interests’ where they are not.
The processing of Special Category Data (previously called ‘sensitive personal data’) requires an additional legal basis. For the processing of Special Category Data for archival purposes, a Data Controller should rely on Section 4(a) of Schedule 1 of the Data Protection Act 2018 – ‘necessary for archiving purposes… in the public interest’.
Note that ‘consent’ as defined by the legislation, allows the data subject the right to request the deletion of the recording. This becomes particularly difficult in group interviews. You can either explain the lawful bases on the participation agreement or you can refer people to your organization's privacy policy if it covers the collection of oral history interviews.