In the US, divorce laws varied (and still do) by state. Nevada became the divorce capital of the nation by repeatedly passing legislation that made its divorce laws more liberal than any other state. This process began at the turn of the twentieth century in partial reaction to Progressive-era trends, but also in response to an ethic of the West with demographic roots: with few women in many Western communities, women gained the power in the nineteenth century to be more selective about whether to remain in or leave a marriage.

As other states (particularly Western ones) passed more liberal divorce laws, Nevada legislators realized that they were losing an emerging "divorce-tourism" industry, and so they passed a succession of even more liberal divorce laws. This culminated in 1931, with the Great Depression: the Nevada legislature passed laws that legalized gambling and liberal divorce laws that were not equaled for many years in any other state.

"Liberal divorce laws" were defined by two factors: the first was the reasons one could seek a divorce and the other was the length of residency required before seeking a divorce. The first issue meant that anyone - husband or wife - could seek a Nevada divorce without the consent of the spouse, and they could seek a divorce for things including "mental cruelty," which means that no cause other than "I'm not happy" was sufficient.

By decreasing the time of residency in Nevada, Legislators persistently out-competed neighboring states that were shortening the time spent in the state before applying for a divorce. There was a problem here: to shorten it too much meant that the "divorce tourist" would not linger in Nevada and spend a lot of money, so the amount of time authorized in Nevada was always sufficiently shorter than that of neighbors to attract the business, but not too short to deprive local hotel owners of the income.

This legislative cat-and-mouse game persisted for several decades in the early to mid-twentieth century until something closer to no-fault, same-day divorce became the norm in Nevada. By 1965, the laws of several Western states were sufficiently liberal that Nevada could no longer count on the divorce industry for as much income; instead it focused on easy marriages - something that had always been there, because where there is a divorce, there is often a marriage. This gave rise to the cliche of the Las Vegas wedding ceremony officiated by an Elvis impersonator (or an ill-conceived marriage as a consequence of a bachelor party gone bad). Capturing the last days of the divorce industry, John Huston's famous film, The Misfits (1961), features the last film appearance of both Marilyn Monroe and Clark Gable: at that time, the divorce industry was still alive and well, but it was beginning to fad in importance because people were able to go elsewhere for quick, easy divorces.

While the Nevada divorce industry faded by the mid-twentieth century, Nevada divorces were still coveted by residents of states with particularly difficult divorce laws. New York, for example, still sent unhappy people to Nevada for divorces because of restrictive legislation that meant that vindictive spouses could still make it difficult for a disgruntled person to find freedom. I cannot speak to the specifics of divorce laws of states other than Nevada, however.

I'm even less familiar with the divorce laws of the UK: early in the twentieth century, there were examples of UK residents coming to Nevada for divorces, but I don't know of the status of that trend by 1965.