It is notoriously difficult to positively identify geographical sites from Arthurian literature: there are allusions in the landscape from Cornwall to Scotland; but one site that does seem to fit is Lud’s Church as the location of the Green Chapel from the late 14th century poem Sir Gawain and the Green Knight.
Sir Gawain and The Green Knight
Gawain is King Arthur's nephew and a Knight of the Round Table who appears early in the development of the Arthurian legend. Gawain is a major character in the Arthurian section of Geoffrey of Monmouth's Historia Regum Britanniae, where he is a superior warrior and potential heir to the throne until he is tragically struck down by Mordred's forces.
Sir Gawain and The Green Knight is a late 14th-century verse romance, 2,530 lines long surviving in only one manuscript, written by an anonymous author usually referred to as the Pearl-Poet, (or the Gawain poet) because it is found in the same manuscript as other works Patience, Cleanness, and Pearl. Another unattached poem, St. Erkenwald, may also be by the same poet. The author was a well read man and he’s moral consciousness of sin, guilt, penance, and forgiveness suggest he was probably a cleric, possibly a monk from nearby Dieulacres Abbey, just North of Leek; the dialect suggests a North Staffordshire location.
Sir Gawain and the Green Knight features the beheading game, which became popular in French Arthurian literature around the time of Chretien's Perceval and a similar version features in Livre de Caradoc, but the tale has its roots in much earlier Irish tale Bricriu's Feast. The poem also has elements of the chastity test which featured in the tradition of Arthurian literature in tales such as Robert Biket’s Lai du Cor (Lay of the Horn, ca. 1250-1300). Another, later version of the tale is The Boy and the Mantle, in which a magical item is brought to the Arthur’s court which can only be used by a woman who is faithful to her husband.
Bricriu's Feast appears in early Irish Knights of the Red Branch literature, part of the Ulster Cycle, and has been dated to the early 8th Century, by far outdating any French grail literature so we can be certain the beheading theme has its roots firmly in Celtic mythology.
In brief Bricriu’s Feast is a series of episodes describing various tests of valour which the three bravest warriors, Cu Chulainn, Conall and Loegaire, have to undergo to determine who is most worthy to receive the Champions portion at a feast prepared by Briciu of the Poison tongue:
Cu Chulainn, Conall and Loegaire were the most courageous fighters in Ireland so to decide which of these was the greatest and who would take the Champion's Portion at Bricriu's Feast. To determine who was the greatest warrior a giant named Uath, termed a Bachlach, challenged them into a beheading game. Each warrior in turn would be allowed to behead the giant, but face his axe the next day. Conall and Loegaire did not accept this challenge but Cú Chulainn did and beheaded the giant. The giant stood up and retrieved his head and left. The next day, the giant returned with his axe and demanded that Cú Chulainn kept to his word. Cú Chulainn placed his head on the chopping block but twice the Bachlach could not behead because his neck was too short and the chopping block too small. On the third attempt he swung his axe but brought it down on Cú Chulainn’s neck but blunt side down. He declared Cú Chulainn was the bravest of the warriors then disappeared. The bachlach turns into Cu Roi in disguise who had come to fulfil his promise to Cú Chulainn 
Cu Roi appears in several Irish Tales as a semi-supernatural figure, scorcer and shapeshifter, most frequently in the guise of a giant or herdsman. He helped the Ulstermen on a raid of the Underworld.
The beheading game would later reappear in the tale of the Arthurian legend as Sir Gawain and the Green Knight and has many similarities with Bricriu’s Feast and Morgan le Fay, the scorcer, is substituted in the English tale in place of Cu Roi.
The poem is set in the days of King Arthur at the New Year's feast at Camelot:
The feast is interrupted by a huge green knight who challenges any member of the court to deal him a blow that is to be returned at his home, the Green Chapel, twelve months later. Sir Gawain beheads the knight, who picking up his head reminds Gawain of their agreement and leaves. At Michaelmas, Gawain sets off for the Green Chapel. He journeys through North Wales, through the Wirral to the North Midlands. On Christmas Eve, he is invited by Sir Bertilak to stay at his castle which is near the Green Chapel. Sir Bertilak and Gawain agree to tell each other each evening what they have gained during the day. Sir Bertilak goes hunting and Gawain has to resist the temptations of the seductive Lady Bertilak. On the third day, Bertilak has only managed to catch a fox while hunting, so gives Gawain the pelt. Gawain does not present the lady's gift, a magic green girdle which makes him invulnerable. On New Year’s day, Gawain rides to the chapel to meet the green knight who takes two swings with the axe but only nicks Gawain. On the third swing he cannot cut off Gawain's head because of the magic girdle. The knight reveals to him that he is Sir Bertilak and that the whole episode was planned by Morgan le Fay.
The tale gives graphic detail of the butchering of a deer caught while out hunting. The poem also contains pagan elements with reference to the annual cycle of death and rebirth and the three attempted axe cuts may be referring to the triple death associated with merlin or druids, the Celtic obsession for the number three.
The Green Chapel has been identified as Lud’s Church because of the poet’s use of dialect words and rare topographical terms used in the poem appear in place-names all very local to the Roaches and this area of the Staffordshire Moorlands There is further evidence in the poem:
“…..Then the lord quoth, laughing, "Now must ye needs stay, for I will show you your goal, the Green Chapel, ere your term be at an end, have ye no fear! But ye can take your ease, friend, in your bed, till the fourth day, and go forth on the first of the year and come to that place at mid-morn to do as ye will. Dwell here till New Year's Day, and then rise and set forth, and ye shall be set in the way; 'tis not two miles hence.
Then the knight spurred Gringalet, and rode adown the path close in by a bank beside a grove. So he rode through the rough thicket, right into the dale, and there he halted, for it seemed him wild enough. No sign of a chapel could he see, but high and burnt banks on either side and rough rugged crags with great stones above…..
………Then he drew in his horse and looked around to seek the chapel, but he saw none and thought it strange. Then he saw as it were a mound on a level space of land by a bank beside the stream where it ran swiftly, the water bubbled within as if boiling. The knight turned his steed to the mound, and lighted down and tied the rein to the branch of a linden; and he turned to the mound and walked round it, questioning with himself what it might be. It had a hole at the end and at either side, and was overgrown with clumps of grass, and it was hollow within as an old cave or the crevice of a crag; he knew not what it might be……” 
• High banks on either side:
the valley of the Black Brook between the north side of Back Forest ridge and Gradbach Hill,
• Rough rugged crags with great stones above:
this fits the general location of the area, the Roaches perfectly,
• a bank beside the stream where it ran swiftly, the water bubbled within as if boiling:
The confluence of the River Dane and the Black Brook runs swiftly and appear to bubble over rocks,
• The mound:
Lud’s Church is on the spur of the hill, not easily seen amongst the vegetation but appearing as a mound from the path
• had a hole at the end and at either side:
Lud’s Church has openings at both ends,
• was overgrown with clumps of grass:
Lud’s Church is overgrown with clumps of grass and vegetation clinging to its rocky sides,
• it was hollow within as an old cave or the crevice of a crag:
Lud’s Church is hollow inside like a cave or the crevice of a crag and is in fact marked on OS maps as a cave,
• 'tis not two miles:
Swythamley Hall is less than two miles from Lud’s Church.
Gwalchmei: the Hawk of MayIn Welsh Arthurian literature, Gawain is considered synonymous with the native champion Gwalchmei ap Gwyar, who appears in the Welsh Triads and in Culhwch and Olwen, an 11th century Arthurian tale but probably much earlier, making him along with Cai and Bedwyr amongst the earliest characters associated with Arthur. Here Gwalchmei, like Gawain, is Arthur's nephew and one of his chief warriors; Arthur sends him and five other champions with Culhwch to find Olwen.
It has been said that the the sun only shines directly into Lud's Church at midday on the summer solstice. But the poem refers to an event on New Years day, so it is referring to an event around the winter solstice, which would, however, appear directly opposite the summer alignment.
Gwalchmei may have originated as a Sun God of Celtic myth; in the later Romances Gawain is shown to have the extraordinary ability to grow stronger towards midday before waning in the afternoon; his might triples by noon, but fades as the sun sets. Gwalchmai has been translated as the Hawk of May.
Also contained in the early Arthurian story Culhwch and Olwen, is Gwynn ap Nudd, Lord of the Underworld, who abducted a maiden called Creiddylad after she eloped with Gwythr ap Greidawl, Gwyn's long-time rival. King Arthur settles the feud by arranging for the two to battle every May Day until Doomsday, Gwyn and Gwythr's fight, which began on May Day, represented the contest between summer and winter. This sounds very similar to Gwalchmei as the Hawk of May waxing and waning with the power of the sun and may demonstrate his origin in the pantheon of Celtic gods.
Knight’s Lowe in the grounds of Swythamley Hall has been suggested as a possible site of Gawain’s grave. However, William of Malmesbury said that the tomb of Walwen (Latinised version of Gawain) was discovered on the sea-shore, in a certain province of Wales called Rhos, which is understood to be that still known by the same name, in the county of Pembroke, where there is a district called in Welsh Castell Gwalchmai  and in English Walwyn's Castle.
“At that time [1066-87] in the province of Wales known as Ros was found the tomb of Walwen [Gawain], who was the by no means degenerate nephew of Arthur through his sister. He ruled in that part of Britain which is still called Walweitha and was a warrior most famous for his courage; but he was driven from his rule by the brother and the nephew of Hengist, though he made them pay dearly for his exile. He shared deservedly in his uncle’s praise, because for several years he postponed the collapse of his tottering homeland.
However, the tomb of Arthur is nowhere to be found—that man whose second coming has been hymned in the dirges of old. Yet the sepulcher of Walwen…is fourteen feet long. It is said by some that Walwen’s body was cast from a shipwreck after he had been wounded by his enemies, while others say that he was murdered by his fellow citizens at a public feast.” 
Walwyn's Castle was built within an Iron Age hillfort at the head of a long narrow valley running north for 3 miles from the Cleddau estuary, Rhos, in the modern day waterway of Milford Haven. Built on an inland promontory formed by the divergence of the valley, the roughly triangular site had steep slopes on two of its three sides and steep rampart on the third. It was later re-fortified by as a Norman motte and bailey.
In the Stanzas of the Graves a similar locality is indicated:
"The grave of Gwalchmai is in Pyton,
Where the ninth wave flows." 
Maybe Gawain was beheaded after all, Caxton, in his preface to Malory's Morte Darthur, writes:
"In the castle Dover, ye may see Gawaine's skull"
1. Ancient Irish Tales. ed. and trans. by Tom P. Cross & Clark Harris Slover. NY: Henry Holt & Co., 1936
2. A Companion to the Gawain-Poet, “Landscape and Geography" - R Elliott pp. 105–117, DS Brewer; 1997.
3. Sir Gawain and the Green Knight - prose by Jessie L. Weston, used for ease of reading.
4. Gwalchmai was the original name from Welsh tradition which appears in some of the earliest welsh literature such a s Culwch ac Olwen before the French romancers changed it to Gawain.
5. William of Malmesbury: De rebus gestis regum Anglorum. (Book 3, chapter 287) in Arthur’s Britain, E K Chambers.
6. Pyton is considered to be Perditon, or Perrydon, in South Wales.