Impossible Creatures by Katherine Rundell

Christopher is stunned when he discovers a passage to the Archipelago: a cluster of magical islands where all the creatures of myth still live and breed and thrive in their thousands. There he meets Mal: a girl from the islands, who is in possession of a flying coat and a baby griffin, and who is being pursued by a killer. Together they embark on an urgent quest to discover why the creatures are suddenly perishing, voyaging across the wild splendour of the Archipelago, where sphinxes hold secrets and centaurs do murder, in a bid to save both the islands and the world beyond them from a rising evil – before it's too late.