Interesting that your version comes from Salford.

This is what my mother sang to me when I was very small:

There is a happy land, far far away,
Where little piggies run, three times a day.
You should see those piggies run, when they see the butcher come.
He cuts slices off their bum, three times a day.

My mum was born in Lowestoft, and I'd always imagined she got these words from Suffolk folk - but, as she'd married a Lancashire man, we lived in Lancashire. So perhaps she learned it, as a young wife, in Lancashire...