Beowulf is more Scandinavian than primitive English, so why does the British poet tell the story?
The vague historical aspects of the epic would have occurred around 516 A.D.
In 575 the Swedes descended south into Geatland. (The prophecies at the end of the poem refer obliquely to these events.) The Geat ships coming back couldn't land, so some made their way to England, Northumbria especially, and settled there, bringing in their stories which were passed down orally.
The poem was composed, after the transmission of several separate legends maybe, about 750 A.D. One wonders if the situation involved a monk writing in the "mirror for the young prince" mode -- in other words, writing to promote heroic virtues to be emulated by the young male(s) of the household.
The transcription of the Beowulf manuscript is dated at about 1000 A.D. Two scribes were probably involved, but we have only the one manuscript. The manuscript itself has had as interesting and harrowing adventures as Beowulf ever did.

The Beowulf Manuscript:
The best medieval manuscripts were made of vellum (involving uteruses of unborn lambs, and so pretty exclusive). Otherwise you get parchment. The monasteries were the libraries and storehouses, but also the first place you head for when you're a marauding Viking. They usually moved west in the spring, and would raid, pillage, and burn. So it's no small thing for any manuscript, much less the Beowulf manuscript, to survive a millennium. Mold, rats, leaky roofs, ignorance, using manuscripts for fish and chips -- there are countless ways for them to disintegrate.

We have four manuscripts of entirely Old English works: Beowulf, Exeter, Vercelli, and Junius. There are no references elsewhere, so we really don't know what we have here or how representative they are.

Henry VIII was the next greatest sinner for his destruction of the monasteries. Not until the end of the 17th century did interest in collecting old manuscripts begin. Sir Robert Cotton started a bit earlier in 1625, and some of the seemingly technical ms info one sees at the beginning of scholarly editions can be demythologized here. Beowulf is "Cotton.Vittelius.A.xv." Cool, huh? But all this means is that it was in Cotton's library where he had plaster busts of the ancients decorating his bookcases -- so this manuscript could be found in the bookcase that had the bust of Vittelius, on shelf A, slot 15. Not exactly the Library of Congress system.

The British government purchased the manuscript since, after all, it was realized that this was a national treasure, and for safekeeping they transported it to, get this, Ashburnham House in Westminster. In 1731, no surprise, Ashburnham House burned to ashes. The fire consumed all printed books stored there and about 200 of the 900 manuscripts. Beowulf was injured but survived.

In 1787 a Dane named Thorklin started making a copy of the document, now at the British Library. A transcription was ready for the edition in 1807, at which point the manuscript was compared. Thorklin had more than the manuscript. In other words, deterioration was rapid.

In the Napoleonic wars the house containing the manuscript was bombed. In 1815 the edition finally came out. By now one needs ultraviolet light, the ink has faded so much.