This is a reread, but I first read the novel so long ago that I'd forgotten most of the plot. All I remembered was an English girl (Tini) on a Greek island channelling the goddess Athene, and Pethi (her Greek friend) with his cat riding on his shoulder. (I have fond memories of trying to persuade the cats at home to do this. I may also still have some scars.)
A Circle of Stones, like its sequel Five from Me, Five from You, is set on the island of Serifos, the birthplace of Perseus. McDonald's writing is clear, not condescending (I wonder if children today would find it difficult, as they apparently find Rosemary Sutcliff's writing hard work) and unaffectedly poetic: the 'swearing tremble' of a cat's growl, for instance. She balances the beauty of the island -- blue skies, white houses like sugarcubes tumbling down the hill -- with the grinding poverty that sends most of the men abroad, because there's no work.
Pethi has a secret which might make all the difference to the islanders. George, Tini's father, is an archaeologist who'd love to share that secret. And the man who owns most of the island's mines is scheming to close the mines and make his fortune another way. Vleppo (the aforementioned cat) plays a major role in thwarting those schemes. (I'd forgotten just how much violence there was in this book. I'd forgotten just what Vleppo does.)
Rooting around on the web, I find there's another children's novel, No End to Yesterday, by Shelagh MacDonald -- but it's set in the 1920s. I suppose she'd written all she wanted to write about Serifos, Pethi and Tini. I do wish there was more.