WAV:

Take a look here and tell me if you see any reference to "English Flute" that is more than a suggestion that it might have been an alternative name for a brief period?

Also: how many people do you see/hear calling the transverse flute a "German Flute" these days?

Neither was really the formal name of the instrument. Composers in the 17th and early 18th century when they specified "flauto" on a score usually (but not invariably) meant a recorder. If they specifically wanted a transverse flute they would specify "transverso" on the score. The latter term died out during the 18th century as the recorder fell out of use as an orchestral instrument and "flauto" became the normal term for a transverse flute. When the recorder was revived in the late 19th century, then another name was found for it and so it has been called since.