This is a really interesting question, though unfortunately I don't think we have a definite answer.

For starters, the question isn't really one of "technology" so to speak. I'm not completely familiar with the origins of eclipse prediction, but the knowledge dates back to at least ancient Greece and was never lost to the West. At basically any point in Medieval Europe, SOMEONE could predict an eclipse.

The question is made more difficult, however, because of the location and time. After the departure of Rome in the 5th century, we have precious little knowledge of what Britain looked like in the next centuries. The Chronical record doesn't really pick up until Bede's Ecclesiastical History of the English People in 731, which itself has some reliability problems.

Now what does this have to do with Eclipses? Well, the question, as I said before, isn't "Did the astrological know how exist?" it's "did the 6th century residents of the British isles have access to it?" (And I'll note that I'm avoiding ethnic specificity because the scale, timeline and methods of the displacement of the Briton kingdoms in favor of Anglo Saxon ones is super controversial) So, the question of "what is the state of Classical learning in 6th century Britain" is really germane to the problem at hand.

So, back to Bede, it's pretty clear that he had access to a substantial collection of Latin texts, as well as some more recent writings, and he seems to have corresponded with other ecclesiastics to get information for his history. It's certainly at least possible, therefore that he or another colleague could have had access to a text detailing how to predict eclipses, but unless someone with better Latin than me can cross reference the texts we know they had, there's no way to confirm that. And even if that comes up dry, there were certainly more texts there than we know of. So that's a solid maybe.

But here's the problem: A Saxon prelate in 731 is not a Briton Lord in 528. The already thin record for the 8th century is all but nonexistent for the 6th. Does that mean fewer people were reading, or is it a matter of luck and age that nothing from that period survives? (The whole textual corpus for old English fills about a single shelf, max, so there's plenty of room for outliers) Were the libraries Bede and Co. had preserved from the Roman days in an unbroken scholarly chain or were they mostly imported after things settled down? I don't really have answers to these questions, but I think it's fairly likely that for most of the Anglo-Saxon period, if you didn't know how to predict an eclipse, you probably knew it could be done in principal.