The Fisher King makes the statement he's been waiting for a very long time, a new time to be ushered in... The time of the once and future king. In 1958, the novel "The Once and Future King" by T. H. White was published chronicling King Arthur's youth and education.
John Hurt, Colin Morgan, Angel Coulby, Anthony Head, Richard Wilson, and guest stars Warwick Davis, and Donald Sumpter have all been guests on Doctor Who.
Warwick Davis (Grettir) and John Hurt (Voice of the Dragon) have roles in the Harry Potter series of films. Warwick Davis plays Professor Flitwick and Griphook, and John Hurt played Ollivander. This episode has another tie to the Harry Potter films as well. In the films, Dumbledore has a phoenix as a pet, while in this episode, the phoenix stone is seen.
While there can be a lot of creative freedom when it comes to fictional fantasy content, there are some differences in the anatomy of these mythological beasts. Wyverns have, two legs and two wings. However in this show the Wyverns depicted have four legs and two wings, this would make them small Dragons not Wyverns at all.