Oh, yes, there were alternatives--but not for lesser crimes.
"Hanged by the neck until dead" was standard sentencing language for executions in the UK until 1948. By that point the expression was archaic. But the interesting thing is, while "hanged by the neck until dead" can't really be said to change meaning in and of itself, the expression managed to stay relevant for a surprising number of centuries as the broader context of capital punishment shifted around it.
In the late Middle Ages into the early modern era, the spectacle of punishment--petty and capital alike--was a key component of deterrence, of teaching people what things were crimes and how bad various crimes were, and of building and maintaining public sentiment against criminals and for government and order. Among other things, this philosophy led to a dazzling array of public and gruesome execution methods. The most relevant in this case is the infamous "drawing and quartering" that was used particulary for nobles convicted of high treason.
Drawing (removing entrails) and quartering (what it says on the tin), you see, were actually the later steps in a longer punishment. It may well have begun with burns from hot pincers while being processed to the site of execution (and yelled at, mocked, thrown shit at, etc by jeering crowds). But the key intermediate step was to be hung by the neck enough to strangle and suffer but not die. The point was for the poor sinner to be still conscious as their intestines were ripped from their body.
Over the course of the early modern era, the philosophy of deterrence-through-spectacle held firm, but public tastes of what was acceptable did not. Joel Harrington's The Faithful Executioner describes a similar, actually a bit earlier, shift in the Holy Roman Empire. In England, it specifically took the form of shifting the execution method for The Absolute Worst Cases (I think not necessarily high treason anymore) to being "hung in chains" or "hung on a gibbet." This is burying the lede a little. This means of execution, like drawing and quartering, also began with slow, incomplete strangulation by hanging. Rather than blood and gore, however, it finished by fire.
Gibbet versus neck until dead was the dichotomy in play in the mid-18th century, when the Murder Act (1751/52) both codified a popular contemporary practice and completely upended older practices of deterrence by spectacle. Not, notably, by rejecting the philosophy. Rather, by making one heck of a devil's bargain.
You might be familiar with the--race? competition? scavenger hunt?--among medical students and medical schools at the dawn of modern medicine to acquire bodies for dissection. Well, a most popular and reliable source of newly deceased, non-rotted dead bodies was executed criminals! The Murder Act provisioned said bodies for dissection...public dissection. That's right. The public at large was invited to witness Science! and medical students learned how to be doctors--while the broader agenda of criminal control and public order was, in theory, being reinforced in people's minds.
Although this practice had been occurring for quite some time, its codification/acceptance in law brought to the forefront a confounding biological-ethical issue: how do you know when someone is dead?
Indeed, what was a dissecting doctor to do if the corpse was "not dead yet" suddenly? Were they an agent of justice, or was this a sign that God wished to spare the prisoner? Was it more merciful just to finish the job if the heart was beating but there didn't appear to be consciousness? What were the responsibilities to attempt resuscitation (from the verrrrry late 18th century) under the Hippocratic Oath versus being a good citizen? So doctors would talk about half-hanged and truly dead and other terms that could only ever have imprecise meanings. In this sense, "hanged by the neck until dead" represented a hope and an ideal, and camouflaged a messy reality. Indeed, the "science-ification" of capital punishment has a history far longer than modern attempts to medicalize and clean it up with 'lethal injection'--and a history fraught with just as many moral and medical problems.
Further Reading: