There is strong evidence for the broad circulation of Arthurian literature in C14. There is a lot of evidence to suggest this literature permeated society, partly because of the continuation of an oral reading culture that helped spread information beyond the literate.
Chivalric literature (mostly comprised of anonymously-authored poems/romances about King Arthur) spread the myth of Arthur beyond that established in the prose chronicles. These poems have an inherently hybrid character - although typically composed by and about the nobility, this literature circulated much further.
For example, The Awntyrs off Arthur has survived in full in four separate manuscripts, each produced in different parts of England - from London to Yorkshire. This diversity in origin, as well as the unusually high number of surviving copies, indicates a text that experienced much popularity.
In other cases, with poems such as The Weddyng of Sir Gawain and Dame Ragnelle, there is scribal evidence that the poem itself emerged from an oral culture - potentially modified, or composed by an illiterate poet/bard. The textual transmission of Arthurian literature does support an impression of broad circulation, with examples appearing in the libraries of the nobility (such as Sir John Paston's inventory of 'Englysshe bokis' - see p 517) or as dog-eared, heavily-thumbed copies with evidence for transcription from oral accounts.
SOURCES: Rochester's TEAMS and Camelot projects are fantastic resources for Middle English scholarship. Particularly Thomas Hahn's detailed introductions to many of the poems, listed by their central characters.
As an extra point - as well as physical manuscript evidence that these stories were broadly circulated, the tales themselves play off an audience's knowledge of earlier versions of the Arthurian myth (further suggesting the continued interest/relevance of this literature throughout C12-15).
Take Gawain, the son of Arthur's wife. Among the most famous Arthurian poems is Sir Gawain and the Green Knight, which presents a Gawain whose reputation precedes him. Earlier versions of Gawain, particularly from the French tradition, characterise this hero as sexually voracious (such as Gauvain in the C13 Vulgate Cycle, which is even more hostile to the character than Chretien de Troyes' late C13 romances).
But by the time we reach Sir Gawain and the Green Knight in late C14, the characters of Arthur's court have become deeply informed by other literary accounts, letting the author really play around with expectations of Gawain. The poet lets the noble Gawain of the English tradition clash with the ladies-man Gauvain of the French tradition. Rather than face a trial of arms, Gawain's challenge is to resist the sexual approaches of his host's wife - simply put, Gawain must fight against his own earlier reputation.