Thank you very much for taking the time to reply to me, Judith. The archive catalogues at the offices you mention don't appear to contain the burial registers for Barnstaple Cemetery.
I live near London and will be in Barnstaple only briefly over a weekend, so will in any case have no opportunity to visit the North Devon Record office during opening hours.
I have an Ancestry subscription, but there is nothing useful there, or anywhere else I've searched online, so I am hoping someone with local knowledge may be able to help.