The Freddie Mercury biopic took home the trophies for best film drama and best drama actor for its star Rami Malek, who played the late frontman.
Despite being heavily tipped and nominated for five prizes, A Star Is Born took home just one award - best original song for Shallow.
Green Book was the night's other big film winner, scooping three prizes.
It won best musical or comedy film, best screenplay and best supporting actor for Mahershala Ali.
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