I believe there is a copy of at least one episode of 'As I Roved Out' in the Irish Traditional Music Archive.
It's a homemade recording on cassette.

Here are the ITMA identifier numbers for the cassette

CID: 49680
ITMA Reference:        3356-ITMA-CS

Title:        
General Music. Cassette 114. Recording of BBC radio broadcast and field recording of music and singing [sound recording] / [various performers]

Contents:        
[Recording of BBC radio broadcast, 'As I Roved Out'. Featuring Seamus Ennis]