Walt Disney Presents All the Songs from Winnie the Pooh and the Honey Tree. Disneyland DQ-1277, 1965. (on vinyl, second-hand)
Not the same versions of the songs that are in the cartoon, although it is at least Sterling Holloway singing Pooh’s songs. In case you’re confused: no, there aren’t enough songs in “Winnie the Pooh and the Honey Tree” to fill an album. The record is 16 minutes long, including three versions of the theme song and (I think) extra verses added to some songs to pad them out.