In order to produce a coherent sentence, its meaning must be clear -not ambiguous. There are two problems with this sentence, "The wind blew just as we were drinking tea with increasingly fury."
Problem 1: The prepositional phrase " with increasingly fury" is misplaced. Misplaced modifiers are words, phrases, or clauses that appear to modify the wrong word or words in a sentence.
[Were we drinking tea with increasing fury or was the wind blowing with increasing fury?]
Problem 2: The word increasingly is an adverb and in this prepositional phrase it should be written in adjective form or "increasing".
Revised Coherent Sentence:
The wind blew with increasing fury just as we were drinking tea.