It was tenuous when it was first established. It became less so over time. Nothing happens all at once. If the North Koreans suddenly decided they wanted to ape the rule of law and passed a whole bunch of laws and killed a bunch of people French Revolution style, I would hesitate to say that the new nation has rule of law for at least a hundred years, unless I lived there and could observe the process directly so I could ascertain whether they're moving overall towards robust rule of law or more towards modern Russian oligarchy.
From the Restoration to now the complete immunity of the monarch to civil and criminal law has been given; and its only in the mid-20th century that British law recognized some claims against the monarch's government being of-right rather than by-license.
The idea of the monarch being subject to the law was more of a momentary, fleeting, and swiftly violently repressed concept in English law that had already been generally repudiated in England itself when the idea got raised as part of the Revolutionary propaganda in some of England's American colonies a century later, rather than something that was tenuous when first proposed in England but which later became firmly established.
(To the extent Britain has made progress in the rule of law, accountability of the chief of state to the law is pretty much the worst place to look for examples; the bloodshed on both sides of that issue has led to most subsequent progress in the direction of rule of law focusing on making the monarch irrelevant to the law in anything other than a symbolic sense rather than accountable to it.)
Many, many important battles have been fought to change the nature of power between state and nation to form a real difference from the normal state of affairs. That is what I'm arguing is the real crux of the matter.
I can't think of any reasonable standard where England actually has subjugated the head of state to their laws and is also the first to have done so by that standard.
I mean, surely we aren't holding up the military purge of Parliament that produced the Rump Parliament and that Rump Parliament's creation of the "High Court of Justice" and its prosecution of the King as an example of the rule of law... At best, that would give the English credit for the creation of the revolutionary kangaroo court (and, even at that, it probably wasn't original.)
And, even if you were to credit that as establishing the rule of law (and certainly, a lot of the language popularly used -- e.g., in the US's own revolution -- about the relationship between the monarch and the law stems from that prosecution and the propaganda around it), you'd have to recognize that that was hardly a durable principle established in England, having been somewhat forcibly repudiated when everyone who participated it that was caught by the post-Restoration government having been executed for their participation in it.