Miles Hendon is a practical and levelheaded character, and I do not think that he actually believes much of what the hermit says.
Miles knows for a fact that Edward has been at the hermit's house, because he has seen "his very footprints" leading to the door. When the hermit says that the boy is doing an errand for him, Miles recognizes it is a lie, because he knows that Edward, believing himself to be a king, would never put up with "such an insolence" as would have been evidenced by the hermit ordering him to run an errand; "he would not go for (the hermit) nor for any man". Although Miles acts as if everything is explained when the hermit declares he is an archangel, I think he is humoring the man. His only concern is to find Edward, and to do this, he must have the hermit's cooperation (Chapter 21).
Miles knows that the hermit has seen Edward, and is determined to do what it takes to get the boy back. He goes with the hermit on what he later calls "a fool's journey all over the forest", and when the hermit finally realizes that he cannot "get rid" of Miles, he brings him back to the house and goes to fetch the boy. Miles speaks wryly of the hermit as "old Sanctum Sanctorum", and his sardonic manner seems to indicate that he never really took the eccentric holy man seriously. He was just doing what was necessary to get the boy king back (Chapter 25).
Miles believes the king reluctantly because his story is truly preposterous, yet, with his discerning nature, he is drawn to the boy. Even though he acts as if he believes the hermit, I think he is humoring him in order to achieve his objective