In a timely fashion

Hello! Can someone please tell me the origin of the phrase "in a timely fashion"? A person from the U.S. has stated in the forum of another site (not language-related) that it's an "American phrase".

"Timely" is a very old word. In its meaning as "occurring at an appropriate or fitting time," the Oxford English Dictionary has traced it back to the beginning of the 13th century. In its meaning as "early" or "not late," it is similarly old. "In a timely fashion" is a perfectly standard phrase, with no idiomatic nuances.
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