I found a similar story in a newspaper clipping (available during the IAJGSG Conference on one of the paid sites). I have attached the article from the St. Louis Post Dispatch in 1910.
Apparently, my very proper Great Aunt Rose tried to elope with the love of her life, Herman B. Gotteib in 1910. Her mother grabbed the couple, took them home, called the Rabbi, and there was a small wedding at the house that evening.
This is all very far away from the Liverpool registry office, but the article mentions that six of Rose's first cousins had already eloped. Rose was born in Latvia.(Rachel Poole mentions that part of her family was from Latvia, too.)
I wonder if we are overthinking this. I wonder if young couples at the beginning of the Modern New Era of the Twentieth Century just wanted to skip some of the ornate rituals of a very traditional Jewish wedding. Having a Rabbi at the Registry office might be a simple compromise.
It's not proof, but something else to consider.
Peggy Mosinger Freedman