My version, from my Auntie Belle in Clitheroe, Lancashire, late 1950s, is very similar to Chris Guest's but with more of a flourish at the end:

When I were a lad as big as me Dad,
I come out of a pea swad,
Pea swad were so full,
I came out of a roaring bull,
Roaring bull were so fat,
I come out of a gentleman's hat,
Gentleman's hat were so fine,
I come out of a bottle of wine,
Bottle of wine were so clear,
I come out of a bottle of beer,
Bottle of beer were so thick,
I come out of a knob stick,
Knob stick wouldn't bend,
I come out of a turkey hen,
Turkey hen wouldn't lay,
I come out of a lump of clay,
Lump of clay were so nasty,
I come out of an apple pasty,
Apple pasty were so good,
I come out of a lump of wood,
Lump of wood were so rotten,
I come out of a bag of cotton,
Bag of cotton set afire,
And blew me back to Jeremiah.

Jeremiah, blow the fire,
Puff, puff, puff!
First you blow it easy,
Then you blow it rough.
Jeremiah, blow the fire,
Puff, puff, PUFF!