Skarsgård's role in the Norwegian family drama "Sentimental Value" has previously earned him an Oscar nomination, a Golden Globe and an EFA (European Film Academy Award).
Now the award for best supporting actor went instead to Sean Penn for "One Battle After Another."
Composer Ludwig Göransson added a BAFTA statuette to his collection of awards for the music for the vampire horror film "Sinners." Earlier this month, he also won two Grammys for the same film.
BAFTA, the British Academy Film Awards, is Britain's equivalent of the Oscars and is usually seen as an indicator of how the Oscar statuettes will be awarded in March.
The gala is underway.
