Paul - the great Burl Ives? Your mother had good taste in music. I first heard it from Steeleye Span. There’s a more recent version by Bellowhead - excellent (I’m not a fan of Finbar’s Furey’s singing, despite being Irish!).
I read St. Anne is the guardian of young maidens and the song requests her to be ‘away’, so that the girls might ‘dance the polka’, and spare Jack from the perils of streetwalkers.