Briefly stated, historians don't think that Bede who was writing in the 730s had accurate knowledge of what happened in the 450s, nor are we certain that he particularly cared. He was much more interested in making sure that England was included in something called "salvation history" (hence his central story about the Synod of Whitby has many parallels with the Council of Jerusalem as described in the Acts of the Apostles). The story about the Angles, Saxon, and Jutes was a much more recent invention that fit well with Bede's storyline, so he happily used it, whether or not he thought it was true.

Combining the few scraps of texts with the massive amounts of archaeology done on early England gives a radically different picture. There wasn't invasion, but there was a total economic collapse in the 400s. I think the best explanation is that all the regular legionary units got pulled from Britain to fight in the civil wars of the late empire (probably even before the so-called Rescript of Honorius from 410), which meant that Britain got cut off from the southern economies: no legions meant no government subsidized shipments from wealthy Mediterranean trade centers to Britain and no government contracts for Britons to supply legionnaires.

The super elite probably abandoned Britain altogether. On the one hand, the lowest classes may have even benefited somewhat from this tax relief. On the other hand, government subsidized industries like iron extraction and leather making may have disappeared entirely as well, dramatically reducing the material wealth of these post-Roman Britons.

The peasants look like they moved to easier soils. This produced less of a surplus, but they didn't need a surplus because there were fewer taxes. Plus it meant they could spend more time working on the household crafts necessary to survive in the absence of Roman markets, making things like homemade cloth and tools.

This produced a situation where outsiders could move in and settle on very fertile land, albeit land that was harder to work and gave its owners less time to tend to household comforts. There was a slow and probably continuous migration back and forth with the Continent. Gradually, the Britons and their new neighbors from the Continent came to share a common material culture that looked Germanic. This shouldn't come as a surprise, since that's the way that the Roman military elite had already been moving during the late empire. In Britain, this culture grouped into a few basic styles, which followed the major riverways of the island: the Thames, the Severn, and the Trent.

Later authors like Bede could reflect on these three areas of material culture, its Germanic and non-Roman tendencies, and they're remembered stories of migration. The story about the Angles, Saxons, and Jutes must have been a very compelling explanation for the things that people living in 8th-century Britain could observe about themselves. So although the Britons vs. Saxons story is trumped up far beyond what actually happened, it also can't be dismissed as pure hogwash.

I'd strongly recommend reading through a few other posts on this subreddit, and most especially the comments by /u/alricofgar:

• Where were the Anglo Saxons truly from?

• Why did the Angles, Saxons, and Jutes decide to migrate to Britain? Was it "easy pickin's" or did they have some previous connection to the Isle?

• When the vikings were attacking the British Isles, were the Anglo-Saxons living there aware that they, too, were descended from Germanic people who had gone to England a few centuries prior?

I am not an expert, and my sources are scant, but most of what I know about this topic comes from the British History Podcast, with some smatterings of primary sources and articles.

Piecing together the narrative on Bede alone doesn't really give us much to work with; we also need to look to archaeology and what transpired before to get a fuller picture. But thinking of Anglo-Saxon occupation of Britain (or to be fair, mostly England) as an invasion scenario is probably incorrect. Archaeological evidence does not point to a terrible lot of armed conflict at the time, and certainly no one single Angle or Saxon group colonized the country in a monolithic event.

Rather what seems to be the case is a gradual, mostly peaceful agricultural colonization, with Romano-British displaced or simply melting into the new Anglo-Saxon population. It's tempting to think of the Roman citizens as being better outfitted and more organized than the Germanic peoples who were migrating, but the population of Britain was never majority Latin speaking, and it appears that a large chunk of the Romanized population of Britain migrated to mainland Europe in the time surrounding the fall of Britain.

The Romans who left caused a massive hole in the economy. Roman economy relied on trade and specialization throughout the Empire, so many villages were, for instance, dependent on the creation of pottery and got other necessary goods from elsewhere in Roman trade networks. After the Roman population left these places, increasingly those left had to turn to subsistence farming, as supplies from the Empire proper were growing scarce. This scarcity also applies to military resources, and with a shift from more densely populated towns to manorial estates it was also more difficult to recruit for centralized armies, as had been the previous system. Fortifications became less common, and new buildings were made of cheaper timber and thatch, because sourcing all that quality stone and then building with it is a more labor-intensive, specialized profession. Meaning maintenance of existing Roman structures, which were being abandoned in droves because a town economy was no longer viable, was not only not a priority, but not really a possibility either.

Speaking to actual settlement, let's talk about Germanic incursions. Raiding most certainly took place, but from Roman records these seem to be less large scale armies compared to what one would see in mainland Europe. In fact, the first Anglo-Saxons to settle were most likely INVITED by the Romano-British as mercenaries, and given land for their trouble. In the contemporary records we have we don't really see any single state trying to conquer large swathes of territory. It's more a situation of raiders going, "hey, it's pretty nice farmland here, let's just settle." And subsequently inviting their friends and family over to join them, increasing the Germanic population.

It's only after the Anglo-Saxons arrive and have been settled in for a couple generations that we see drives for increasing the size of all of these new kingdoms. The Britons themselves had not stayed united and were broken up into their own little kingdoms as well, but it's not as if they were the sole targets of Anglo-Saxon expansion; these kingdoms were just as often at odds each other as the Britons. Eventually all of England is Anglo-Saxon ruled, the Britons under them assimilating the culture. What remains of the Romano-British culture and kingdoms are Welsh, a word which somewhat amusingly is rooted in the Germanic for "foreigner."

You mention that you imagine the Britons having better technology. Could you talk a little more about that? It's not something I'm familiar with.