That's an atrocity bluecliff! I wish I'd know you had one I would have saved it. This was one of the best movies of the 20th century. And the song is a beautiful classic Irish lullaby.

Edit: Welsh lullaby, not Irish. I'd be cursed at profusely if I made that mistake in the UK.

Great band...I'll join you HOju! No need to chase this one down...

http://www.videosift.com/video/Drunken-Lullabies-Flogging-Molly

In case anyone is wondering.... the music is actually from mario 64: Piranha Plant's Lullaby. or at least really damn close to it. so im a nerd and the song was more appealing to me

Link: http://www.vgmusic.com/music/console/nintendo/n64/Asleep.mid

*edit: their version is from the OST. mine is but a crappy midi. up vote only for music selection

Dom Joly picks out all the music himself from his own record collection, apparently. The ones i recognise:
The maze: Starsailor - Tie Up My Hands
The gorilla: Dodgy - Grassman
The farmer and the badger: The Verve - Lucky Man
The Chinatown tour: The Beta Band - Dr. Baker
The big fish: The Cure - Lullaby