The 31-year-old took on the role of Elvis in the recent biopic of the legendary musician, and won big at Sunday’s ceremony.
The gong comes just weeks after the sad death of Lisa Marie, the singer’s only child – who was laid to rest at his Graceland estate in Tennessee last month.
Speaking in the winner’s room, the actor revealed that it was a ‘bittersweet’ moment to take home the trophy after such a tough time.
‘It’s been a really unimaginably tragic time,’ he told PA. ‘Grief is a long process and so my heart and my love is with them always.
‘And I feel honored to have been welcomed into the family. It’s a bittersweet time.’
Lisa Marie died in January at the age of 54, with her mother, Priscilla Presley, confirming the sad news.
‘It is with a heavy heart that I must share the devastating news that my beautiful daughter Lisa Marie has left us,’ she said in a statement.
‘She was the most passionate, strong and loving woman I have ever known.’
Just days before her death, Lisa Marie attended the Golden Globes where she watched on as Austin won the best actor award for his portrayal of her father.
Elvis, directed by Baz Luhrmann, delved into the life and career of one of the biggest singers in history, and also starred Tom Hanks, Olivia DeJonge and Helen Thompson.
The acclaimed flick scored three other wins at the Baftas – for best costume design, best hair and make-up, and best casting.
‘Besides Baz, there’s hardly anyone that was by my side more than Polly was,’ he told Metro.co.uk.
‘She was the person who, if I couldn’t sleep at three in the morning and was obsessing about this one performance – I couldn’t sleep so I’d watch this bit of footage and I’d call Polly and she’d always be there.’
‘She was my rock during that time and we were also in Australia for a long, long time. I was there for over a year and a half and so we became like family in that time,’ he stated.
‘I can’t quantify how much that she actually did. I couldn’t have done it without her.’
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