From what I understand, Finland was quite peripheral to early medieval politics and would not be settled by Scandinavian people until some centuries after. It surprised me that an English writer would be familiar with Finland, even if describing a story set in Denmark.
Were there trade networks between England and Finland at the time Beowulf is set (6-7th century) or the time in which it was written (10-11th century)? What contact existed between these two end-nodes of the Scandinavian cultural sphere?
Well, there are a few premises here that have to be examined. Firstly whether Beowulf's "Finna land" actually refers to Finland, which it certainly does not in the present-day sense of the term. "Finn" in English in today's sense is essentially a re-borrowing of the same word from later Swedish usage.
It's an ancient Germanic word. It's etymology is uncertain and so are its early meanings, as the earliest uses are from Mediterranean second-hand (at best) accounts. Tactius writing around the year 100 AD has the fenni in Latin, and some decades later there's Ptolemaios writing φίννοι. Both their accounts are much too vague to say who the terms actually refer to. By the time we have sources, in the Viking Age (~800-1100), the term has taken on different meanings among different Scandinavians. Norwegian or the West Norse dialects were using it to refer to Sámi people, while Swedes or East Norse dialects were using it to refer to people of Finland-Proper, which is the area near Sweden on the southwest 'corner' of the Finnish mainland. The term "Finland" in its present day sense evolved later as a pars-pro-toto. Viking Age Norsemen diligently distinguished different the different Finnic groups of present-day Finland (Finns, Tavastians, Karelians, Savonians, etc)
It's theorized the term originated as a broader term for people living nomadic lifestyles; one clue being the region Finnveden (ON Finnheiði - Finn-heath), attested as far back as Jordanes Getica (mid 500s). Neither Finns nor Sámi are known to have lived there, but it's a rather isolated forest region.
So who did the term refer to in Anglo-Saxon? And who did it refer to in Beowulf, specifically?
Beowulf's people are the Geatas. There has actually been some debate about which group this term refers to; but majority opinion has always been on the side of the Götar (in modern Swedish; Old Norse Gautar). The etymology is pretty straightforward, with Old English "ea" coming from a Proto-Germanic "au" that remained "au" in Old Norse and became "ö" here. (c.f. "bread, dead" to Swedish "bröd, död")
Still, some have argued for other identities, most recently the archaeologist Bo Gräslund made his case in a book for why he thinks Beowulf was a Gute, that is someone from the island of Gotland off the Swedish coast and a distinct people.
The Götar were one of the two major peoples of present-day Sweden in the Iron Age, distinct from the Svíar (Swedes-proper, Svear in modern Swwdish) who lived in the regions around lake Mälaren and today's Stockholm.
Beowulf's Sweones are considered to be Swedes/Svíar (and it's in this sense I'll be using 'Swedes' henceforth). This identification is more certain. The name Sweoðeode for their country has its close counterpart in Old Norse Svíþjóð. And the names of some of their kings are mentioned: e.g Eadgils and Othere, which are traditionally equated with the Yngling kings Aðils and Óttarr mentioned in Norse sources.
As reflected in provincial names to this day, the lands of the Götar and they themselves were divided into western and eastern parts (Väster/Östergötland), depending on whether their waterways lead to the Baltic or to the Atlantic, as the drainage divide was at the border. But the story does not include this distinction, much less specify which kind of Geat he was.
Västergötland is usually the main contender, based on its proximity to Denmark (where he travels in the story) and for that matter the British Isles. But if Beowulf was returning home to Västergötland, it would be very unlikely he'd end up in Finland(-Proper.) But it would not be very likely he'd end up in the Finnmark of Norway either. Going off course and ending up in Finland on returning to Gotland or Östergötland is much more probable.
But another question is, should we put any stock in Beowulf's geography to begin with? Perhaps not. The main reason for alternate theories of the identity of the Geatas, despite the low-odds etymological connection to Götar is that the poem is geographically inconsistent. As said, there are no west/east-Geats They are described as being separated from the Swedes by a great sea, which is a key selling point of the Gotland theory (and also more far fetched proposals, like Pomerania), while Västgöt-proponents have rationalized it as lake Vänern.
If we look beyond Beowulf, the even older Anglo-Saxon poem Widsith lists a laundry-list of peoples, where the Finns are also mentioned "Casere weold Creacum ond Cælic Finnum" (Caesar ruled the Greeks and Cælic the Finns). It was suggested in the 19th century that "Cælic" here would be a corruption of Kalev, from Finnic mythology. But given the supposed corruption and the fact that this mythology isn't recorded until a millennium later, it's highly uncertain.
So this would seem to do little to establish who the Finns here are, either. A better indication in favor of the Finns-Proper is that the poem has a mentions peoples of the Baltic region in particular, such as the Hælsings (dat. pl. Hælsingum), which is almost certainly the people of Hälsingland, the coastal region along the Gulf of Bothnia, north of the Svíar and opposite the Finnish coast.
In summary, most readings give Finland-Proper as the most plausible reading of Finna land. So now that we're back where we started, what does that say about Anglo-Saxon contacts with Finland?
Not that much, necesarily. For starters we don't really know who wrote Beowulf. Was it even a single author? Was it an original work based on preexisting oral myths? (And to what extent?) Or a translation of a Scandinavian original?
The dominant view has long been that it was an original by a single author (a recent stylometric analysis concluded the same, too). This author knew at least something of Nordic peoples, and Widsith shows that such knowledge had been transmitted. A minority position with a long history, and most recently advocated by Gräslund again, is that it is however a translation from a Scandinavian original text.
We don't know when it was composed either; virtually any time between 600 and 1100 has been suggested by someone at some point. Even in recent scholarship you'll find claims as divergent as 11th century (Damico 2015) and 8th century (Ecay and Pintzuk).
Nevertheless, in the time when the story is set (and before and after) there were still close contacts between present-day Finland and Sweden, even if these intensified in the Viking Age and eventually culimanted with the expansion of the Swedish state into the area not long after its emergence at the end of the Viking Age. Particularly Uppland, the core region of the Svíar and close to Finland, had such contacts going very far back (The Alunda moose is a beautiful stone axe from around 2,000 BCE from Uppland, and of presumed Karelian origin) There's ample evidence from archaeology of interactions in the Migration Period and Vendel Age (550-800), but also linguistic evidience in the form of loans from Proto-Germanic/Proto-Norse. (e.g. Finnish kuningas is from PGmc *kuningaz rather than Old Norse konungr or medieval Swedish konunger)
Likewise there's evidence of Anglo-Saxon-Norse interactions in the period; a perennial example of which is the similarity of the Sutton Hoo helmet (and grave) to the contemporary ones from Vendel and Valsgärde in Uppland. There's a history of even more explicit connection-making between Beowulf and Sutton Hoo, too (e.g. by Lindqvist 1948 who was the one who excavated Valsgärde).
There's not much evidence of direct contact; Anglo-Saxon coins do not show up in Finland until the Viking Age, and those likely got there through Norse intermediaries. (the much higher proportions of German coins in Finnish Viking age hoards relative Scandinavia indicate they did do their own trading, but more locally)
But with ample evidence of cultural contacts from East Anglia to Uppland, it's not that surprising that knowledge of the peoples around the Baltic would be transmitted there and/or preserved.
Aaron Ecay, & Susan Pintzuk, _The Syntax of Old English Poetry and the Dating of Beowulf, in Neidorf et al. Old English Philology, Boydell & Brewer, 2016
Helen Damico, Beowulf and the Grendel-kin: Politics and poetry in eleventh century England. West Virginia University Press, 2015
Bo Gräslund, Beowulfkvädet: Den nordiska bakgrunden, Acta academiae regiae Gustavi Adolphi, nr 149, 2018
Sune Lindqvist, Sutton Hoo och Beowulf, Fornvännen 1948, p94-110
I’m going to just add a small piece regarding the second part of your question in answering was there any contact between the Anglo-Saxons and what we consider “Finland” today/and was there any knowledge of such regions. /u/Platypuskeeper ‘s answer does a wonderful job at considering the term "finns" with regard to Beowulf and its geographic/ethnographic constructions, whereas this will focus on what/where we imagine Finland as today.
In two extent manuscripts at the British Library - Additional 47967 (c. 9th-10th c. CE), and the Cotton Tiberius B. i (11th c. CE) – a travel narrative of the Accounts of the Journeys of Ohthere and Wulfstan are found attached to Old English translations of a Paulus Orosius’ History Against the Pagans in Seven Books which was composed in the 5th c. CE. The appendage acts as a sort of periplus (a document which outlines information regarding coastal landmarks) which gives what seems to be a genuine eyewitness account of various regions and cultures in the Baltic Sea as well as the North Sea, as far northeast as the Kola peninsula, into a region known as Bjarmland.
The narrative seems to be from the perspective of Wulfstan, an explorer who travelled with the Norwegian merchant Ohthere, and it is being presented to King Alfred:
Ohthere told his lord, King Alfred, that he lived northernmost of all the Norwegians. He said that he lived by the western sea [the Atlantic Ocean] in the north part of the land. He said, though, that the land extends very much further north, but it is all wasteland, except that the Sámi camp in a few places here and there, hunting in winter and fishing in the sea in summer.
In this context as far as I can tell finnas is referring to the Sámi people, and as /u/Platypuskeeper has shown in their answer, is different to any reference to “Finns” in Beowulf. Here is a further extract of from the narrative of the journey along the northcoast of Scandinavia and Finland:
He said that on one occasion he wished to find out how far that land extended due north, or whether anyone lived north of the wasteland. Then he travelled close to the land [modern-day Norway], due north; he kept the wasteland to starboard [the right-hand side of the ship] and the open sea to port [left-hand side] all the way for three days. Then he was as far north as the whale-hunters ever travel. Then the land turned due east – or the sea came into the land – he did not know which; he knew only that there he waited for a wind from the westnorth-west, and then sailed east, close to the land – he did not know which. Then from there he sailed south, close to the land, for as far as he could sail in five days. A great river extended up into the land there. Then they turned up into that river because they dare not sail beyond the river for fear of hostility, because on the other side of the river the land was entirely settled. Previously, he had not met with any inhabited land since he left his own home. But to the starboard side there was wasteland all the way, except for fishers and fowlers and hunters – and they were all Sámi; and there was always open sea on his port. The Bjarmians [from the Old English Beormas] had cultivated their land very well [I think this is referring to the “other side of the river” that is settled], but they dare not put in there. But the land of the Terfinns was all waste, except where hunters or fishers or fowlers lived.
The Bjarmians told him many stories both of their own land and of the lands which were round about them; but he did not know what the truth was, since he had not seen it for himself, The Sámi and the Bjarmians, it seemed to him, spoke almost the same language. He travelled there chiefly – in addition to exploring the land – for the walruses, because they have very fine bone in their teeth (they brought some of those teeth to the king), and their hide is very good for ship-ropes. This whale [walrus] is much smaller than the other whale: it is no longer than seven ells long [about four metres]. But the best whale-hunting is in his own land: those are forty-eight ells long (about twenty-seven metres], and the largest fifty ells long [about twenty-eight metres]. He said that, as one of six [of the whalers], he killed sixty of those in two days. He was a very wealthy man in that property of which their wealth consists, that is, in wild deer. When he visited the king, he still had six hundred tame animals unsold. They call those “reindeer”; of those, six were decoy reindeers. They are very valuable among the Sámi because with them they capture the wild reindeer.
He was among the chief men in the land. Nevertheless, he had no more than twenty cattle, and twenty sheep and twenty pigs, and the little that he ploughed, he ploughed with horses. But their income is chiefly in the tribute that the Sámi pay them. That tribute consists of animal skins and in bird feathers, and whale-bone, and in the ship-ropes which are made from the hide of whales and seals. Each one pays according to his rank. The noblest must pay fifteen marten skins, and five reindeer skin, and one bear skin, and ten measures of feathers, and a bear- or otter-skin coat, and two ship-ropes, both to be sixty ells long [about thirty-three metres], one to be made of whale’s hide, and the other of seal.
