The whole significance of the trial for which it is so widely studied is apparently the insight that desuetude basically doesn’t exist and laws are effective until they’re repealed. But then what is desuetude and where does it fit in? Is it a more recently developed doctrine?
On the contrary, desuetude is the older idea. The newer one is that acts of the legislature remain fully effective, up to the time that some other statute repeals them (directly or by implication). In the English conception, Parliamentary sovereignty means that a judge could not overrule Parliament. That applies equally to an old law as to a new one. The Crown also lacks power to suspend a law - certainly since the Glorious Revolution.
The cited case is an example used to illustrate the strength of the English constitutional principle, but it did not establish that principle. It is just a striking example of judicial willingness to follow the written intent of a Parliament from three centuries prior. (See below for which Act I am talking about.)
The notion of desuetude is more familiar to the law of Scotland, where the courts are less willing to give total prominence to statute law. The theory derives from Roman law, as described by Salvius Julianus (excerpted in the Digest at 1.3.32; translation by Alan Watson, 1998),
For given that statutes themselves are binding upon us for no other reason than that they have been accepted by the judgment of the populace, certainly it is fitting that what the populace has accepted without any writing shall be binding upon everyone. What does it matter whether the people declares its will by voting or by the very substance of its actions? Accordingly, it is absolutely right to accept the point that statutes may be repealed not only by vote of the legislature but also by the silent agreement of everyone expressed through desuetude.
That said, the principle was most easily applied to private rather than public acts, as a form of estoppel. The typical example is if a law gave some power to a burgh, such as licensing of tradesmen; it would be unjust if they suddenly started enforcing it after many years of neglect, even if that power was contained in a statute. But desuetude can extend even to statutes of a constitutional nature. There were many Acts concerning appeals from the courts to Parliament, a process called by the incredible name "falsing of dooms". But that entire procedure fell into desuetude even though it remained in some sense "on the books".
Desuetude also requires not only a period of non-observation of the old law, but some active practice that conflicts with it. And it is not applicable to post-Union statutes, which represent the vast majority of statutes currently in force.2
From the case report of Ashford v Thornton (1818) 106 ER 149, there was much argument about the conditions relating to "appeal" (that is, private prosecution) of murder, since there were many rules and circumstances even before any "battel". The entire procedure was one known to the many common-law writers cited before the judges - Bracton, Fleta, etc. - but also regulated by statute. In particular, there are many references to an act of 1487, cited there as "3 Hen.7 c.1", which dealt with the topic.3
That act, which would not be repealed until 1948, was mainly about coroners' investigations of deaths, but it also expressly referred to the concept of private appeal. For example, it says
yf yt fortune that the same felons or murdrers and accessaries so arrayned, or eny of theym, to be acquitte [...] the Wyf or next heire to hym so slaine, as shall require, may take and have theire appelle of the same dethe or murdre, within the yere and day after the same felonye and murdre don, ayenst the seid persones so arrayned and acquitte
which in modern language means that if the official inquest found somebody to be not guilty, then the wife or next heir of the victim could still pursue an appeal.
Since this statute had not been repealed, it would seem that appeal was a process that could be followed. And the nature of that process was known to the common law, as described above, even including a potential battel. The conclusion may be surprising. The presumption of the system is that Parliament is always able to change the law if it does not like the consequences, as it did soon after - 59 Geo III c.46, "An Act to abolish Appeals of Murder, Treason, Felony or other Offences, and Wager of Battel, or joining Issue and Trial by Battel, in Writs of Rights".
1 "Nam cum ipsae leges nulla alia ex causa nos teneant, quam quod iudicio populi receptae sunt, merito et ea, quae sine ullo scripto populus probavit, tenebunt omnes: nam quid interest suffragio populus voluntatem suam declaret an rebus ipsis et factis? Quare rectissime etiam illud receptum est, ut leges non solum suffragio legislatoris, sed etiam tacito consensu omnium per desuetudinem abrogentur."
2 It does still come up sometimes. In 2010, the Court of Session held that an act of 1532 stating that "na man enter to pley, bot parties conteined in their summoundes and their procuratoures, gif they will ony have" was not in desuetude, because it had been considered still alive as recently as 1984. A case in 2006 to the contrary was said to have been wrongly decided.
3 Boring citational footnote: This is divided as 3 Hen. VII c.2 in the modern version of Statutes at Large, where "c.1" is about the juridical power of the Star Chamber. Ruffhead's original version joins them together. The original text from the Rolls of Parliament would not have been divided at all.