Also, She hates scratching dogs is ambiguous too?
closed as unclear what you're asking by Adam, SamBC, Nathan Tuggy, shin, RubioRic Mar 4 at 8:12
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Yes, both statements can be interpreted in two ways.
English can be understood to modify either history or professors.
and scratching can be understood to refer either to her action or to that of dogs.
To clarify these statements, they can be rewritten as:
Professors of English history....
British professors of history....
Professors of history in England....
English-speaking professors of history
although the last two raise other concerns.
She hates dogs that scratch
She hates to scratch dogs