This seems to have been a circle game like Ring-a-Round the Rosie.

Round About, Round About - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Intro Image

Notes

*Maggotty pie is an obsolete word for magpie – which is a type of European bird.

Here's a version of this song from The Only True Mother Goose Melodies (published and copyrighted in Boston in 1833 by Munroe & Francis):

Round About, Round About, Gooseberry Pie

Round about, round about,
Gooseberry Pie,
My father loves good ale,
And so do I.

Thanks and Acknowledgements

The first version of the song can be found in A History of Nursery Rhymes (1899) by Percy B. Green. The 2nd version of the song and the illustration are from The Only True Mother Goose Melodies (published and copyrighted in Boston in 1833 by Munroe & Francis).