I'm interested in all the historical accounts, if any, where the Bible was forbidden/censured to be read, by order of secular powers in the Christian world, i.e. mainly Roman Empire or the Byzantine Empire. I vaguely know of two instances, neither of which I can confirm if true. One regarding Code of Justinian, where supposedly Emperor Justinian only allowed the clergy to read the Bible (again I'd like to confirm this), second was of King Henry VIII of England, before the Reformation, persecuting the Tyndale translation.
This question suffers under a couple of misapprehensions I think.
The first one is that there's a single unitary "The Bible" out there somewhere.
What we have is translations drawn from copies of older sources. These older source copies themselves, being hand copies, all have differences with each other. Which ones are "right"? Take your pick between "we don't know", and "none of them are".
Also, language translations are inherently interpretations, so anything that isn't in the older source's language should be considered a paraphrase. Or to put it in Paul's terms, we are only seeing through a mirror, darkly.
So its much more accurate to ask about specific compilers/translators Bibles. For example, possession of Wycliffe's Bible could get you executed in Henry IV's England. The Catholic Church also wasn't a big fan of the translation choices in the Tynedale Bible which seemed to downgrade the need for organized church hierarchy. They finally hit on the idea of fighting fire with fire, and produced their own translation (The King James Version) which was intentionally more biased towards authoritarian institutions like the King and the Catholic Church.
The second misapprehension is that there was a canon "Bible" from go. In fact for the first 4 centuries everyone just copied around the stories that they found most useful, and some of them said quite contradictory things to some of the others. At the end of the 4th Century the church set down a definitive "Canon", that left a lot of this stuff out. Some of it we know as apocrypha, but some of the more troublesome stuff, particularly the Gnostic Gospels, were actively suppressed. If you were a Gnostic at this time, from your perspective, yes they'd just made your "Bible" illegal to read. They'd also excommunicated your leaders though, so you might have bigger problems than reading.
There are different approaches to such a broad question — if anyone wants — to answer 'yes', which are defensible.
To address one example given in the question:
the popular notion that the laity was forbidden to read the Bible in English under late medieval law […] misunderstands the Oxford Constitutions of 1408, which merely prohibited the making of new, unauthorised translations of the Bible.
— Jonathan Reimer: "Thomas Cranmer. By Susan Wabuda. Routledge Historical Biographies, New York–Abingdon: Routledge, 2017".
If we just look for any 'secular power', then an American school board may fit the bill quite nicely. Albeit this is somewhat a struggler over definitions in more than one way, one example might be:
— William W. Boyer: "The Bible in Wisconsin Public Schools: A Forbidden Book" Religious Education, 55:6, p403–409, 2006.doi
Of course, the more general approach must look at the universal church, una sancta, especially in the form of what is now known as The Holy Roman Catholic church.
As closely as any match could be to what is hinted at in the question:
We prohibit also that the laity should be permitted to have the books of the Old and New Testaments; unless anyone from the motives of devotion should wish to have the Psalter or the Breviary for divine offices or the hours of the blessed Virgin; but we most strictly forbid their having any translation of these books.
— WP: Censorship of the Bible, with quite some more examples not reproduced here
This is a bit dependent on which bible was prohibited. Having a Vulgate version would be much less of a problem. But this is ultimately based on what exactly the powers that be or were would define as heresy. This of course started with the very first canon — or a bible — that ever came to be in to Christianity.
Marcion of Sinope suggested that a proper bible would be without any Old Testament (thus he was rejecting another bible), but only consist of 'his' Lukanian-ish gospel and ten letters of Paul. While at first a very wealthy and this welcome member to the Roman fold, his ideas turned out to be seen as heretical. The obvious result was that he, his followers and his version of 'the book' were excommunicated and banned. Not so obvious was that indeed he got the money he donated to the church back in the process ;) That after their fallout the remaining Catholics weren't fond of anyone reading that bible seems quite evident in the fact that we have no extant copy of it.