We don't have this one in our collection so the details are a little sketchy. Info online has also been somewhat meager. We do know that the cover artwork was first used in the 1957 US "storyteller" LP (no. ST-3906) which featured the narration of Annette Funicello. This one clearly has the "Told by Annette" notation on the cover. However, the Bambi story from that series was a separate record. It was not narrated by Annette, but instead, by another Mouseketeer, Jimmie Dodd.
These may be those storyteller recordings. However, Disney was known to reuse artwork from older albums, even to the extent of simply trying to use up the old stock before printing new ones. This is conjecture, yet we think this record might simply be the soundtracks to the two films, sans any story narration.
Annette is listed on the disc label in the American edition (left). She is not on the British example. (right).
Then we came across another printing of the record. On the cover, they have blocked out the reference to the"story" aspect of the recording as well as Annette's contribution. Seems like it may indeed be a soundtrack-only record. Maybe someday we'll have an opportunity to listen and know for sure.
Additional images via Discogs.com.
UPDATE: Disney expert Nunziante Valoros has this record in his collection and recently had a listen. He confirms that this is indeed the original soundtrack for both films, as released in the DQ series. It does not contain the Annette Funicello and Jimmie Dodd stories.