Without wanting to piss on your bonfire UP, the chances are slim. Unless it was a super-famous advert, nobody would have gone to the bother of recording it back then and then put it online these days.
Your best hope might be to write to the makers of Beamish and ask them who made it / if they still have a copy of it.
p.s. just found out the word Beamish was invented by Lewis Carroll, so there you are.
p.p.s. the band behind the song, Karla with a K, also wrote my favourite song ever, Satellite -
http://www.youtube.com/watch?v=1lwYK8EHd_M ... it reeks of the 80s but I still like it even to this day.
soz. reminisce over