This was the chant of pig pie vendors. The pigs they referred to were made of paste and currants and were supposed to look like pigs – they weren't real pigs.

A Long-tail'd Pig - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Intro Image

Notes

Some versions of this rhyme have these additional two lines at the end:

Take hold of the tail and eat off his head,
And then you'll be sure the pig hog is dead.

The Little Mother Goose (1912), illustrated by Jessie Willcox Smith, prints this rhyme in an odd way. It has the ending as a "Moral":

A LONG-TAILED pig, or a short-tailed pig,
Or a pig without e'er a tail,
A sow-pig, or a boar-pig,
Or a pig with a curly tail.
MORAL:
Take hold of his tail,
And eat off his head,
And then you will be sure
The pig-hog is dead.

Thanks and Acknowledgements

This rhyme can be found in Harry's Ladder to Learning (1850). The illustration is from The Nursery Rhyme Book, edited by Andrew Lang and illustrated by L. Leslie Brooke (1897). This rhyme can also be found in Traditional Nursery Songs of England with Pictures by Eminent Modern Artists edited by Felix Summerly (1843).