I have a few hundred scores of classical recorder music and quite a few CDs. None of them call the instrument an "English flute" in the title, and I very much doubt whether any publication ever used the phrase in its main title. It was only used for a fairly short time, from 1725 to about 1750, to distinguish it from the traversiere or German flute, but "common flute" was a far more frequently used term. "English flute" was simply a marketing phrase used to convey "you don't need to buy an expensive new transverse flute to play the music in this book, you can use what you've already got".

BTW, one kind of flute I had thought was specifically English was the bamboo pipe, as used in the 20th century make-your-own bamboo pipe consort music movement, which is still just about in existence. But on googling I see the movement started in the US.at around the same time (not an easy thing to search for, you keep getting sidetracked into opium and drains).