Buckfast (a wine tonic brewed by monks) is the drink of choice for the 'ned' subculture (a term originally coined by police to mean 'non-educated delinquent'). 'Ned culture' is so prominent that it not only is is it a massive stereotype, but also features in many comedy sketches. 'Bucky' plays a central role being their preferred choice of cheap booze.
I don't get it but perhaps the pun is contained in this little song:
What do ye get when ye drink the wine?
A ten pound fine an'a year's probation,
A kick in the baws at the polis station.
AWWWwwwww, never drink the wine again!
AWWWwwwww, never drink the wine again!
Yeah, I had to google a bit to make any sense out of it and I could still be wrong. Some would say any pun is not a good pun. I rather like puns though.