I see what you mean about Roy Palmer's introduction - he certainly thought they were there, despite the entry on the EFDSS wiki I quoted.
The Sound Archive search for Burstow returns 6 items, 5 of which are folk-related (one has composer Burstow), and all mention the name in the context of notes (one not Henry Burstow).
Since the Sound Archive helpfully provides contact information, it would be easy to contact them and see if they have any more information:
Janet Topp Fargion
Curator, World and Traditional Music
The British Library Sound Archive
96 Euston Road
London
NW1 2DB
United Kingdom
Tel: +44 (0)20 7412 7427
Fax: +44 (0)20 7412 7441
E-mail: worldandtradmusic@bl.uk
The other avenue would be to see if anyone could contact Roy Palmer and find the basis for his introductory remarks.
Are you volunteering for the treasure hunt Nick?
Mick