Hi KitKat,
Could this be their marriage?
William Constantine, Vol. 19 Page 227 Stockport, June 1840
And on the same page; Elizabeth Williamson - same details.
The certificate would give fathers' names and occupations.
hume 

Edit: From a previous thread (dated last month), I notice you have this information. 

 Think it will be most helpful though in finding William's parents.