Both Catnach and Pitts of London printed it in the early 19th century, but it was printed on broadsides all over the country and even in America under a variety of titles, usually in 7 stanzas, corresponding to 'Cook's Choice' as given above.

The Catnach broadside is at Bodleian, Harding B11(1836) 'Cookey's Courtship or Cupboard Love'.

A later copy printed by Harkness of Preston is on the same website, Harding B20 (73) 'Beef and Treacle or Cook's Courtship.'

'Compliments Returned' has a similar history though not so common in oral tradition. On broadsides it is known as 'I don't think much of you'. This was also widely printed and like the previous ballad printed in New York. Both a Hodges of London and a De Marsan of New York broadsides are on the Bodleian website

Harding B18 (269)
Firth b25 (396)

Longer versions of both these songs were printed by the Glasgow Poet's Box in the 1850s.