This Google Ngram shows that "Why did not I do" is far more common than "Why did I not do", at least in its source texts since 1940, and over 10 times as common as of 2000. This surprises me, I would have said that "Why did not I do this sooner?" " is an old-fashioned form, echoing the language of the King James bible, and of Shakespeare. The inversion of "not" and "I" was once common in formal speech, and I would have said is now rare. But to say that this "is not English" is simply incorrect.
I would nonetheless favor the use of "Why did I not do this sooner?" or in informal contexts "Why didn't I do this sooner?" except when trying to produce a particular stylistic effect.