Seems like they were uncommon until the early 1800s or so. What led to their rise in popularity? Just about everyone has one now (and I’ve got two!).
I believe the practice was adopted from German immigrants, at least in the US. How it got to Britain (and where the Germans got it from) I couldn’t say.
Well, I do not have factual information. Based on their usage to distinguish people, I have a hunch that an element of it was in drawing the same distinction as surnames did earlier: just as you wanted to distinguish between John the Brown-complected and John the Miller, you needed to distinguish between John Harry Brown, the grandson of Harry Thorpe, and John Wesley Brown, the Methodist preacher’s son.
A second element most likely was the longstanding tradition of taking the name of one’s chosen patron saint at Confirmation, common in many churches. Generally such a name was adopted as a second given name, in the place of a middle name.
From over-the-shoulder observation of my wife’s English genealogical research: quite a few of the 19th C middle names are the mother’s maiden name, or a grandmother’s maiden name, etc, rather than the given names of relatives (which seems more common today).
Some of these middle names (originally surnames) then move into common use as first names (generally for boys) and then become first names for girls; Morgan and McKenzie being a couple of off-the-cuff examples.