Blackett and Wilson (Info) apparently identified the body as "King" Arthur, and the cave with one in Coed y Mwstwr ("Wood of the Muster/Commotion") which they describe as partly carved (apologies to Blackett and Wilson if this is inaccurate, this is all taken from websites of various levels of dubiousness - anyone with a copy of their 1980 book, please get in contact). Their suggestion appears to rest on a conflation of the two caves in the Life of St.Illtud*, the second of which is the wonder cave (See Note), and the first of which is given in the following:
King Meirchion was moved with excessive wrath, wishing to kill the innocent man Illtud...[Illtud] seeks everywhere for secret security, where he might hide his face. After inquiring he arrives at length at the bank of the river Ewenny, where he saw a very secret cave. Seeing it, he entered, and occupied it for the space of one year and for the space of three days and nights in addition. The whole night he lay on a cold stone, as he desired, so fulfilling such a penance as he had imposed on himself, as if he were saying, 'This stone for a bed is placed beneath my breast, this is my delight, I will lie down in accordance with the divine will; pleasant will be the blessed reward which will come to one who is blessed, a reward laid up in heaven for me, when I shall reach it...The blessed Illtud prayed then incessantly, fasting daily. Every ninth hour there was sent to him from heaven one loaf of barley bread, and one portion of fish, wherewith he was refreshed. After a temperate meal he visited a neighbouring well, drawing water for himself in the hollow of his hands, as Paul and Antony, the first hermits, performed their drinking. Then he returned to the cave, guarding against being seen by anyone at his entering. He was diligently looked for in woods and in forests, and in the retreats of deep valleys, and was not found after assiduous searchings.
Their identification of the corpse as "King" Arthur seems to rest on their equating Arthur with Athrwys [in older records Atoys?] son of Meurig (See The Returning Plank and Note). This presumably leads them to caves in the area of Glamorgan/Gwent and this one appears to have been carved into an east-west orientation suitable for a Christian burial. Presumably their identification of the corpse as Arthur also rests of the tradition that Arthur's grave is unknown - from wherehence the idea that Arthur will rise again to lead Britain at a time of need (this idea may of course precede the notion that his grave is unknown, but the oldest evidence is for the unknown grave).
As Arthur's grave is traditionally secret or non-existant, it is certainly an attractive idea that the corpse is Arthur's. The oldest reference to Arthur's grave being unknown is probably in the Englynion Y Beddau ("The Stanzas Of The Graves": See Other Works: English Translation) which notes "The world's anoeth a grave for Arthur". The Welsh anoeth is generally translated "Wonder", which may be indicative of our Wonder-list, but it has a broader meaning as something special but difficult to obtain - for an example, see the list of such objects, the collection of which forms the central framework for the tale of "Culhwch and Olwen".
The oldest reference to Arthur still being alive a good deal after he was likely to have died comes from De Miraculis S.Mariae Laudeniensis (1155 CE) in which Herman of Laon describes a trip to the West Country with some Laon canons. Herman notes that a Cornishman said that Arthur was still alive, and got into a fight with Herman's servant over it*. Following this, a post-Gaimar addition to the Estories des Engles (Info) in c.1150 contains the information that the Welsh threatened to reclaim their land from the Normans through Arthur*.
Finally, William of Malmesbury (Info) writing in c.1125 noted that Arthur's grave was nowhere to be found, and therefore that ancient songs predicted his return*: the first extant combination of the two themes, though plainly based on older material. Given the history of Britain since the Dark Ages, one has to question how bad things would have to be to see this particular resurrection.
Conversely to all this, Bridgend Council* quote the following "local legend" about the cave in Coed y Mwstwr:
One local legend has it that, after his death in battle near to Ogmore Castle, King Arthur was secretly laid to rest in a cave in Coed y Mwstwr Forest, just behind the village and close to the Coed y Mwstwr Hotel. His body stayed there and his death concealed for fear that it would split the nation. When his son was old enough to replace him, the death was made known and King Arthurís body was removed from the cave and laid to rest in a grave at Cor Emrys church close to Pencoed.
Though it is unclear to what extent this has been influenced by Blackett and Wilson or vice-versa. There are certainly plenty of tales like it (see, for example, Rhys* On Caves). If independent, it is interesting if for no other reason than it suggests a tradition in which Arthur was survived by a son (cf. details on Arthur's son's under Amr's Tomb: somewhat coincidentally there is a nearby village called LLecheu).
As for the identification of the corpse as Arthur: it is an attractive idea, but not one for which there is any evidence - two mysteries are not necessarily the same just because they are both mysteries. The corpse is described as a "Holy man", or, indeed a "Saintly man" (sancti hominis, cp. the latin for "Saint Iltutus" sanctus Iltutus); whatever Arthur was, the lives of the various "Dark Age Celtic Saints" that have come down to us via Medieval versions almost universally cast him as an unholy foil to display the goodness and power of the saints, and their dominance over the secular hierarchy. While the Historia in the "Campaigns of Arthur" list (See Contents) includes the battle of "Guinnion Castle" where Arthur carried the image of Mary, the mother of Jesus, on his shoulders (possible misreading of Welsh original saying "shield") and the Annales Cambriae (for 516 CE: See Other Works) portray Arthur as carrying a cross at the Battle of "Badon", this hardly marks him out as "saintly" by Dark Age standards.
As for the Coed y Mwstwr cave: while there is much to commend Wilson and Blackett's "Athrwys = Arthur" hypothesis (certainly as much as any other theory: for this and others see here), the cave identification seems a little stretched. Coed y Mwstwr is a good five miles from the sea, at least 20 miles from Gower, and at 50m above sea-level the waves would hardly be lapping around it. While the description of the wonder in the Life of Illtud differs from our description in saying the burial took place in the cave and doesn't mention a church (See Note), the Historia is explicit in mentioning the grave as the site of a church and there is no suggestion of a church around the Coed y Mwstwr cave. Of course, plenty of hermitage caves have small chapel-areas in them and these are orientated east-west where possible, so if the cave has been altered it could be both a burial site and a chapel, but it seems a squeeze. Most damningly, the two caves are explicitly separate in the Life, and both are clearly in different locations. Any conflation would be a supposition beyond the evidence.
In short, whether or not you choose to regard the cave at Coed y Mwstwr as Arthur's mortuary, or Arthur as the mysterious corpse, there is little to link the cave at Coed y Mwstwr with the Wonder in the description, save the figure at the centre of two very different sets of suppositions.