Researching the Vikings, and as a hack medievalist, the thought occurred to me that even in the Middle Ages, Britain is in a strong position if it can be properly developed. Economics are the basis of everything. It would be forced to engage in oversees commerce, which would make it a preeminent naval power, placing it in a position to have long and wide ranging trade routes, a population well trained in sea travel and ship building, and a tradition and infrastructure of ships built for such things. These would develop commerce and interaction across Europe, spreading ideas as well as commercial items, all leading to a benefit for Britain. Innovation would be encouraged by these economic realities and foreign ideas. It could also lead to the infrastructure for overseas expansion and colonization. Imagine if it were the Britons rather than the Norse who discovered Iceland, Greenland and the coasts of North America.
Well, it is a question of how much one wants to wank Britain I suppose. When I realized the span of years required for Roman Britain to luck out and arrive at a date as late as Charlemagne's time as a well-organized, populous and yeoman-prosperous place that could supply legions (adapted to contemporary conditions of warfare) and navies, I felt most of their luck would be used up getting there, and perhaps two or three generations of strong effective Brittanic dynasty Imperium (covering at least Western Gaul, perhaps reinforcing the northern tier of Iberia's Christian refugee kingdoms, extending old imperial borders north past Belgium into northern Frisia and maybe into Denmark) should pretty much drain the rest of it. Something has to come up snake-eyes sooner or later. I'd think Imperial overreach might play a role in the ruin of the great dynasty; British supreme powers won't want to settle for some risky-dink title like Dux or Praetor or whatever; they won't even want to settle for "king." No, they are Emperors now, by right! Clashing with the pope over the title seems al too likely to squander resources and position.
Still, the bigger British power gets in the Arthurian glory days, the more might be left after a considerable fall. I like the idea they fall, but never into utter ruin, and keep bouncing back.
Now regarding sea power, that is always technology-dependent. In OTL Carolingian times, even a Roman administration that scrupulously studied the evolving north seas navigation and maintained a navy of that type would not have ships as seaworthy as the Vikings later did; those innovation were done in Scandinavia and the British would be followers, not leaders in West Atlantic explorations, settlement and trade. To be sure they might know about Iceland long before the Norwegians do, after all it was settled by Irish monks OTL, but what would attract Britons to settle there? Compared to Norway, particularly the northern reaches, and the small islands of the Atlantic on the chain leading to Iceland by that route, Iceland is not so bad; compared to the lands around the Thames in Britain, it is an icebound, rocky treeless hell. The northern islands would be pawns in political games to the British "Arthurs," not refuges. Going west from there the trend seems to go from bad to worse, until news of Vinland arrives, but Vinland is far away, and would be found by Scandinavians, not Britons I would think.
Also, Britain is in the long run vulnerable to waves of conquest as OTL, even if she is stronger than OTL at many points of time. Early interference with Scandinavia, in the great Arthurian age, might butterfly some aspects of Viking expansion, but it might make as many things worse as it makes better. Perhaps the Danes who form the "Danelaw" will already be Christian, but this may not stop them from overwhelming half of OTL England--indeed it might make total conquest of the whole island more acceptable, making the Danelaw universal and an instance of an early Sven and Knut. The establishment of Normandy might go forward as OTL, indeed with the traditional but locally weak king the settlers ofter ostensible fealty to being an Arthur in London rather than a fallen Carolingian in Paris. Normans might, centuries later, seize an opportunity to subdue Britain, and might find extra motive in extinguishing the nominal fealty to the Arthurs and even claiming the title and scope of Arthurian power for themselves--terrorizing the conquered Britons just as they did the English, Frenchifying them, yet in the end winding up Britonized just as OTL they were Anglicized. But such a conquest would turn British interests south and east rather than north just as it did OTL.
Indeed while it has been suggested that an Arthur instead of a Charles would look more northward than the Frankish Empire of OTL did, the very nature of a foundational Holy Roman Empire would tend to draw British interest onto the Continent from the get-go; a Norman Conquest might not be to blame for a more southerly focus of Britain after all, and a Scandinavian conquest or three might fail to break those bonds.
In fact, if Britain is to have any precocious role in discovering or exploiting the New World, I would guess it more likely be by a southern route, by virtue of British sailors discovering islands such as the Azores, and making good their claim and holding them rather than letting the nearby Portuguese claim them. But discovery of the West Indies, and realization of the advantages the Gulf Stream brings for bringing them home to Britain, will all wait many centuries until the art of sea navigation has advanced to at least 15th century levels.