"...the fair and happy realm which the sea took back unto itself..." (p. 44)
sounds like the city of Ys in Poul and Karen Anderson's King of Ys tetralogy but here refers to Atlantis. Thus, the Andersons wrote four novels about one sunken civilisation and Poul wrote one novel about another. The Atlantis of myth, fantasy and much science fiction (sf), including Doctor Who, was a prehistoric civilisation, sometimes technologically advanced, on a mid-Atlantic continent that sank. In some works of fiction, it even survives into the twenty first century as a submarine civilisation whose inhabitants adapted by becoming merpeople.
Apart from the time travel premise that makes it sf, The Dancer From Atlantis is historical fiction and therefore is set not on the mythical continent but on Crete in accordance with the theory that Cretan Minoan civilisation was the source of the Atlantis legend. I am still rereading so have not yet retrieved all the details.
A well written time travel story makes more sense when reread. One such detail is that we know at an early stage that Reid will lose his wrist watch. Erissa says of the watch, "'You did not have this before..." (p. 40).
She remembers meeting him in her youth and he is soon to meet her in her youth.