I would only add that the symbol of King Arthur is almost a religious icon, a Christ-like figure. The legend is that Arthur will one day return (like Christ) and save England. The name Arthur means ‘bear-like’ and since the beginning of the Arthurian legend, strength, nobility and courage have been associated terms. There are other elements of the legend that represent virtuous, and in some cases even modern qualities. One example is the round table, which represents a republic or democratic equality. To make a stretch, the ‘round’ symbol has been associated with feminist iconography; mostly in the 20th century. Was the historical Arthur a feminist? Hard to say; probably not. The point is that so many parts of this legend are applicable to subsequent cultures and historical periods. That’s one reason why Arthur has been written and rewritten over the course of Britain’s history and still is a matter of great interest today. As a symbol of past (and potentially future, conjuring his potential return) hope, Arthur represents the past glory of Britain and the hope of its future glory.
And like the first poster noted, this is all via the medium of literature, so it contributes to Britain’s national and literary identity and promise.
This is a very interesting question. I think that it might strike at an element featured in all of literature and help to bring out a discussion as to why specific examples of literature is deemed important. In its own analysis, the Arthurian legend holds much in way of importance to British Literature: "The Arthurian legend is often referred to as 'the matter of Britain,' and many critics consider it—along with the King James Bible and the work of Shakespeare and Milton—one of the four cornerstones of English literature and culture." In this light, one can see why the legend of King Arthur is so important. It helps to provide a sense of structure and legacy to what England left the world from a literary perspective. The Arthurian legend helped to bring the idea of what constitutes "just" leadership and helped to bring to light how leadership can help guide and propel the advancement of society. The mythology of Arthur helps to prove this. In the end, his importance lies in the literary legacy he inspired through both myth and literature. When examining why the legend is important, it might come down to the fact that what Arthur represents is the very best in terms of character and leadership, something that British Literature chose to display for itself and about itself.