Hardwicke's Marriage Act of 1753 (effective from 25th March 1754) looms large in the history of genealogical research - its full title, "An Act for the Better Preventing of Clandestine Marriage", saying it all. Basically requiring a formal ceremony of marriage, it was precipitated by a dispute about the validity of a Scottish marriage. Curiously, however, the Act only extended to England and Wales, Scottish law remaining unchanged by the shenanigans. One of the greatest ironies in the history of genealogical research, you might say.
What might be described as the defining article on the subject of what brought the Act about can be found in Dr Leah Leneman's effort, namely The Scottish Case That Led to Hardwicke's Marriage Act. It's a piece from an American journal, but penned by an Edinburgh-based expert. Bordering on the academic, I suppose, but worth persevering with.
[I should warn readers that the repeated assertion in the second paragraph by various quoted (and erroneous) sources that the 'first marriage' was overturned in favour of 'wife number two', was not actually how the case resolved itself, as the article eventually bears out.]