Maybe this should be on the other thread, but in respect of the above I've just picked up a first edition of Edgar Hunt's The Recorder and its Music (Herbert Jenkins, 1962), which gives but a single instance of English Flute, and this in a table of names by which the instrument was known. A similar table is reproduced Here, giving the historical window when this name was current, but no indication of just how widespread or common the term might have been.