Is the data being referred to the personal data of the volunteer (and any of their living associates)? Or is it the data about individuals (long dead), that have been transcribed by the transcriber? Or somebody else?

Good question!  It is the personal data of people other than you, that you have for Free UK Genealogy purposes (so emails from your friends and family, etc. aren't covered.  

GDPR only applies to living people, so for most records, it doesn't apply.  
The personal data you need to keep secure will be things other Free UK Genealogy people have shared with you - such as an email asking for help with a transcription, or letting you know that they will be unavailable for a couple of weeks.  No one likes to have personal information such as their email address seen (or used!) by people they did not intend it to reach, but our main concern is that some data we share between ourselves is what the GDPR calls 'sensitive' data:

"...revealing racial or ethnic origin, political opinions, religious or philosophical beliefs, or trade union membership, and the processing of genetic data, biometric data for the purpose of uniquely identifying a natural person, data concerning health or data concerning a natural person's sex life or sexual orientation"

So if the email about being unavailable mentioned the reason as going on a Buddhist retreat, or a hospital treatment, it would contain sensitive data, which might upset them if you told someone about it without their consent.