So this is fundamentally an argument about historiography or the study of how history is made. And this question, and the genetic evidence that these articles muster, can be placed in the context of a broader discussion that has been raging in Early Medieval/Late Antiquity circles for decades.

The best dissection of this debate that I've found is in Peter Heather's Empires and Barbarians where he looks at the different outcomes of the collapse of Roman rule across the former western Empire (and elsewhere) and he discusses the tensions between the two camps, largely that there was significant migration happening in the Late Antique/Early Medieval world, called "mass migration" and the camp that instead favors of model of migration that is termed "elite replacement", wherein a smaller number of people migrated, largely elites who replaced the Romano-British population as the primary political players, or in Heather's words

Many historians and some archaeologists perceive the evident Anglo-Saxonization of lowland Britain in the fifth and sixth centuries to have been brought about through a hostile takeover, which involved large numbers of migrants from northern Germany and the Low Countries. A second group of opinion, on the other hand, sees the process as having been effected by many fewer continental European immigrants, whose cultural norms then spread broadly and essentially voluntarily through the existing population: elite transfer followed by cultural emulation. This is subscribed to by some historians but many more archaeologists, and is obviously heavily influenced by the general rejection of the old mass-migration models inherent to culture history.

The "mass migration" model dates back to the 19th century and has come under fire, but not as much from textual historians, who Heather notes have often landed into the "mass migration" field, but often from archaeologists. Why did this happen? What led the transition in the first place, why has it been discarded, and what do these genetic studies mean?

Let's break it all down.

Our story of the study of Anglo-Saxon England begins in a time long ago and a land faraway (for me). However, it does not begin in England, or Britain if you prefer, in the 5th century. Rather it begins in the United Kingdom in the 19th century.

In the time of rapidly expanding factories, political turmoil, changing economic conditions, urbanization, and more, there were just as divisive and profound changes happening in the world of scholarship and academia. The 19th century was a world that was waking up to many -isms. Among these were socialism, feminism, capitalism, and above all, for our purposes, nationalism. As the world changed and new systems, institutions, and movements developed, people across Europe sought for meaning in the changing world. Some found solace in class struggle, placing their plight in a long continuum of the struggles of the haves and have nots, others in trying to bring about the vote to men, and women, of different races and creeds, but others, many others, looked backwards. Not to the times of the Romans and Greeks, which had been all the rage of the early Modern Period thinkers and the Enlightenment philosophes. It was not Rome, Athens, or Alexandria that most of the nationalist thinkers of Europe looked to, afterall many of the rising powers of Europe at this time, Germany, the United Kingdom, and France, were subjugated by Rome, and while they admired Roman civilization, it was not properly theirs. Their histories, their origins, their genesis lay in the neglected child of the western tradition, in the Middle Ages. After all it was the fur clad barbarians who gave the countries of Europe their names. Britainnia Superior and Inferior became England, Gaul became France, Iberia became Spain, and Italia, well it stayed Italy.

The origin of the major powers of Europe were traced, by their scholars of the 19th century, to the time of Voelkerwanderung or the Migration Age, when whole societies uprooted from their ancestral homes in the primal forests of Germany and Scandinavia and carved out their new homes in Roman territory through a period bloody conquests that left newly formed nations in the wake of Rome's violent death. The infant nations of modern Europe, Germany, England, France, and the others were left standing after the old Classical world burned away in a wave of fire and death.

This is the account that came down to the Victorian, 19th, and early 20th century scholars, and it is not without a good deal of supporting evidence, limited as it is. Textual sources from this time, roughly the 400's-800's are extremely rare, in fact there are about two (there is a third, the "Anglo-Saxon Chronicles, but they are extremely unreliable for this time period as most were compiled starting in the 9th century)

The first is a sermon delivered by a British (Welsh) ecclesiastical figure named Gildas. In his work he describes the process by which Roman Britain, and the British people more broadly, have been laid low by their ungodliness and lack of faith. Their punishment for these grave sins was the invasion of the Angles, Saxons, and Jutes who were the agents of God's wrath upon the wretched and sinful inhabitants of the Island. Only through religious renewal and continued support would the British polities survive and prosper in the face of Germanic attacks. Simple as right? He was roughly contemporary to the events he was describing, the 6th century(ish) and why shouldn't we trust him? Its not like there were ulterior motives for a Church figure to associate the political and economic turmoil of Roman Britain with the wrath of God, right?

His account, while hardly objective was influential enough to survive to be copied in medieval monastic communities where it found its way into the hands of an intelligent monk named Bede, from Jarrow. He used that work, along with other lost works, and perhaps in person interviews, to compile his history of the English people and their conversion to Christianity, which he creatively titled Historia Ecclesiastica Gentis Anglorum or the Ecclesiastical History of the English Nation, and in this work he lays out the ground work of the "mass migration" school of though, basically that the Angles, Saxons, and Jutes all came over from Europe and did some looting and plundering, invited more of their kinsfolk, and ended up pushing out the British and created new kingdoms in the wake of British collapse.

This is the old view of mass migration that characterized the scholarship surrounding the Anglo-Saxon, and Frankish, and many other, migrations into Roman lands up until after the Second World War. Starting in the 1960's though there was a fresh push in looking outside of the traditional sources of knowledge about this time period, and one that emphasized an entirely different source base, archaeology.

Instead of reading through old accounts and taking them at their word, or at least reflective of the real events, starting in the 1960's there were a series of archaeological discoveries that severely challenged the idea of a mass importation of Germanic people into Britain that pushed out the natives in a tide of blood. Their evidence was varied but compelling, and it emphasized the material conditions of Britain.

I can probably provide some clarity on this from a genetic standpoint. During the early years of genetic research there wasn't really any conclusive evidence of large scale replacement of the native population of Britons with Anglo Saxons. Or at least the data didn't real point to a specific time in history when this might have occurred. Since the Anglo Saxons were a specific group, from a specific point in time the conventional wisdom was questioned. One theory was that Germanic peoples were already settling in Britain before Rome collapsed. It was pretty common for the Romans to allow so called loyal barbarians in if they promised to help defend the empire.

Others believed most of the Germanic ancestry came after Rome fell. However, Britain was also invaded by the Vikings later on. Unfortunately there is considerable overlap between the areas Anglo Saxons and Vikings might have originated. There is also a genetic relationship between English and Dutch people which led some people to speculate that perhaps not all of the dark age invaders were Angles and Saxons, but might have been Franks or Frisians who were in the Netherlands. Of course to complicate matters there was a decent amount of Dutch migration to England during the Medieval period. Then there was ever more Dutch migration to England during the European Wars of religion. The point here is that these groups are often so similar and sometimes came only centuries apart, making it very difficult to make any sort of conclusions as to how the current genetic breakdown came to be.

Ultimately you need a lot of skeletal remains that you can with reasonable confidence date to a specific period. But this sort of data and research is just starting to really yield results. So I think you have some historians that were perhaps aware that the historical record was limited and then for a long time the genetic evidence was far from conclusive. So people came up with other theories.

around 75% of the population in Eastern and Southern England was made up of migrant families whose ancestors must have originated from continental regions bordering the North Sea, including the Netherlands, Germany and Denmark

Is that quote from the original study or from the article citing the study?

What the original study seems to say is that "As a result, the individuals who we analysed from eastern England derived up to 76% of their ancestry from the continental North Sea zone, albeit with substantial regional variation and heterogeneity within sites." That is, not that 75% of the population was made up of migrant families but that the population had some members whose ancestry was up to 76% continental.

This answer may not be up to this subs standards, I’m just a measly undergrad, but from what I have read and observed, sometimes in academia people like to overzealously push against older ideas. This oftentimes can be a good thing, but in this case led to a sort of overcorrection from the narrative of a massive invasion of Anglo-Saxon warriors replacing the Britons with the tip of a spear to very few Anglo-Saxons migrating and then culturally dominating the Britons. The truth in my view is likely somewhere in the middle, with both occurring at the same time, ultimately resulting in post migration England having Anglo-Saxon material culture, speaking the Anglo-Saxon language, worshipping germanic gods, and today having a lot of Anglo-Saxon DNA.