I can only guess, Susanne, that what you recorded was a tape made for radio broadcast, probably of a live performance. I'm sure that neither Martin Carthy nor the Watersons have issued "The Hare's Dream" on vinyl or CD.
On the Napster version - which, again, I can only guess was borrowed from a live recording, whether done professionally or not - Martin sings alone, after a spoken introduction in which he points out the song is from the point of view of the fox, not the hunter.
Just when this song was in Martin Carthy's performing repertoire perhaps even he would no longer be sure.
(When I transcribed the words for my site I forgot they were here, so my transcription is genuinely that. I made one correction on the basis of Wolfgang's lyrics - but I'm not sure that Martin sings "to the top o' Sligue". However, as I have no Gaelic - how would I know?)
hth, Garry