The old drunk guy is singing this song toward the beginning of the film "Clockwork Orange".
I figured it must be a real Irish folksong, but for about 20 years I was never sure.
1. In Dublin's fair city,
Where girls are so pretty,
I first set my eyes on sweet Molly Malone,
As she pushed her wheelbarrow
Through streets broad and narrow,
Crying, "Cockles and mussels, alive, alive oh"!