I recently shared his book Elidor with some friends and they enjoyed it. Clearly some of the details in the book are taken from Irish mythology like the four cities of Elidor are the very names of the four cities of the Tuatha de Danaan: Gorias, Falias, Murias, and Findias. The four objects that need to be kept safe correspond to the Four Hallows that the Tuatha de Danaan brought with them to Ireland.
Normally, Garner plunders Welsh literature since he lives near the Welsh border, having lived his entire life in Cheshire. He has admitted to using the Mabinogion for names especially the 'Dream of Rhonabwy'. For the name of Elidor, it appears he has plundered a name and an idea from Gerald of Wales (who I am sure won't mind since Medieval authors did not get as fussed about copyright as authors do today).
While Gerald was touring Wales, trying to drum up support for the Third Crusade, he and his group stayed overnight at Swansea, near the location of a story, which Gerald had been told and one of the local priests had claimed to be the Elidyr of the story. The priest was twelve years of age, at the time of the events, and was hiding from his teacher, whom he was tired of being beaten by (the good ole days!). He was hiding in a hollow bank of a river for two days when two little men appeared to him and offered to take him someplace where it was all fun and games. He went and it was a great place, underground, the people treated him well and he played with the son of the king.
He was allowed to come home and visit back and forth, telling only his mother about the land. She asked him to bring something of gold back for her so he took a golden ball that he used when playing with the king's son. He ran home and tripped over the threshold, dropping the golden ball. The little people, who were right behind him, grabbed it and ran off jeering at him. He never found the way back to the land and eventually went back to his studies and became a priest. When he was old, he told the Bishop of St. David's, who was Gerald's uncle about the story. In response to the question of if he believes the story, Gerald wrote that if he were to reject it then he would be placing a limit on the power of God but he cannot accept it either with any real conviction.
What has this to do with Garner's tale besides the name of the otherworldly land the children must protect? It is the loss of a ball that draws the four children one by one into the ruined church which is the gateway to Elidor. Perhaps it is due to Elidyr's having been a priest that he made the gateway in a church.