As per post, indications are that Cheshire Parish Registers 1538-2000 have have two "intentions of marriage" 1847 and 1849, suggesting such intentions were recorded, but seems images of those entries are not displayed on FamilySearch or FindMyPast websites
FamilySearch for example has 3 different records - with images, for Elizabeth's son William's marriage at Prestbury in 1871, Application for Banns, Banns and Marriage.
Thanks for observation about Elizabeth not being of age (19) in the earlier record. Two weeks after that Parish entry she gave birth to William but had to wait two years to marry the man who was almost certainly the father.
Ssxy