During the Second World War Cook served in the Royal Scots regiment, and in the intelligence corps.
He was a director of the British School at Athens from 1946 to 1954 and professor of ancient history and classical archaeology at the University of Bristol from 1958 to 1976.
Starting in 1969, with his wife, he explored the archaeological sites in Iran, studying the Achaemenid empire.
Cook also drew attention to the similarities between the Carians and the Mycenaeans, "Finds of third-millennium date are confined to a very few points on or near the Aegean coast, with the curious exception of one find-spot which seems to be near Yatağan at the head of the Marsyas valley.
It is now asserted by some scholars that the Carians were a people, perhaps Indo-European, who inhabited the interior of Anatolia and only descended to Caria and the Aegean at the end of the Bronze Age; but this is far from harmonising with the Greek tradition about them, and the writer for one finds it difficult to explain the Mycenaean in Caria (and perhaps adjacent islands) as being anything other than Carian.