Many English novels in the period you refer to involve elopements to Gretna Green, Scotland as a way around restrictive English marriage laws It is a plot element in Sense and Sensibility, for example. The increasing prudishness of 19thC English fiction probably precluded more imaginative fictional treatments. I do recall that there were those who had to go to "the Continent" to marry a deceased wife's sister, in contravention of British law.This link specifically refers to the Marriage Act 1753 in the context of Jane Austen:
The Marriage Act of 1753 also made it increasingly difficult for men and women to marry outside their rank. In cases such as these a couple could obtain a special license from the Archbishop of Canterbury if they were really wealthy, or elope to Gretna Green, which was the first easily reachable Scottish village, where the marriage laws differed from England and Wales.However, the Marriage Act would have been a minor consideration here -- Wickham supposedly intends to "elope" with Lydia in Pride and Prejudice , but it's plain that he doesn't intend to go ahead with any actual marriage unless he's very well paid to do so.
If a couple did elope, it meant that they were unattended until they were married. Normally when a young couple courted they could not be left unchaperoned. If travelling far to elope, a couple would have to stay overnight somewhere, which suggests to everyone that the couple had a sexual relationship before marriage, which was quite scandalous!A more recent US equivalent for elopement to Gretna Green was to run to Elkton, Maryland, the closest place to the New York metropolitan area where you could get married without a blood test. As a true crime fan, I can point to the John List murder case, where List's wife-to-be, who was suffering from latent-stage syphilis, encouraged him to elope to Elkton, where her condition could go undetected. One of the pressures that eventually drove List to murder his family was the tertiary syphilis that emerged in his wife.
Elopement is contrary to natural law.