"No one of" + plural noun phrase

Not exactly, but to understand why and how you need to look at the full Cambridge sentence, which, if my research is correct, is "No one of these properties is unique to adjectives, but only adjectives possess all four."

In that version of the sentence, "one" is setting up a contrast with "all four." In other words, while there is no single one of the properties is unique to adjectives, the set of properties taken all together ARE unique to adjectives.

Similarly, if the Collins sentence set up the children one by one in contrast with the children all together, "no one" would be appropriate: "No one of the the children could speak French fluently, but among them they knew enough scraps to piece together what the letter meant."

Without the second half, the Cambridge sentence "No one of these properties is unique" reads very strangely to me.