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Damien Chazelle won the director award for the feelgood Los Angeles musical.
Chazelle fended off competition from Ken Loach, Tom Ford, Denis Villeneuve and Kenneth Lonergan for the accolade.
The best film was the fifth for the effervescent musical about love and ambition.
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Emma Stone was named best actress for her performance in La La Land.
Damien Chazelle also won the best director BAFTA for the film, which had 11 nominations going into the London ceremony.
La La Land also took prizes for music and cinematography.
The Hollywood musical fended off competition from I, Daniel Blake, Arrival, Manchester By The Sea and Moonlight to scoop one of the most coveted prizes of the night.
