Definitely of interest, Margaret; thankyou.  On the strength of your reference, I had a look at the Bodleian Library Broadside Collection, where, as it turns out, there are quite a few "Jenny Jones" songs; parodies of, answers to, etc., so it must have been pretty well-known.  Here is one:

Jenny Jones  Printed between 1823 and 1834 for B.W. Dickinson of York.

Malcolm