Where a bride (or even groom) was under age -very rare now!- there was usually some encouragement to have the father sign as witness, to demonstrate that permission had been given. From what I recall, minors getting married by licence would always need to get a parent's signature (or witnessed mark), but with a wedding by banns the permission would otherwise be just verbal.
Hi,
From my own personal experience: when I married at St.James Church Norton in 1970 I recall Canon Gleadhill asking for my father's details prior to my marriage. As I hadn't seen my father for several years I didn't even know if he was alive so the information I gave Canon Gleadhill was supposition so my marriage certificate actually states my father's name and occupation though he wasn't actually at my wedding. The marriage was witnessed by my grandfather and brother.