Road movie Nomadland won the top prize at this year's awards, where director Chloe Zhao made history as the first woman of colour and second woman to win best female director.
Nomadland, which tells the story about a woman travelling through the American West, also scooped a best actress prize for its star Frances McDormand.
The most high-profile British winner on the night was Sir Anthony, who was named best actor for his role in The Father, in which he plays an ageing man struggling with memory loss.
It is the Welshman’s second Oscar, coming 29 years after he won best actor in 1992 for The Silence Of The Lambs.
This is the longest gap between wins by any actor in this category in the history of the Oscars.
The 83-year-old also becomes the oldest person to win an Academy Award for acting.
Kaluuya was named best supporting actor for his portrayal of Black Panther party leader Fred Hampton in the the film Judas & the Black Messiah.
Kaluuya is the first British actor from an ethnic minority background to win the award.
His win follows similar success at this year’s Baftas, Golden Globes and Screen Actors Guild Awards.
The writer, actor and director Emerald Fennell had been nominated in two categories for her film Promising Young Woman.
While she missed out on best director, she won best original screenplay, the first British woman to win in this category since it was established in its current form in 1958.
Sir Christopher Hampton was joint winner of best adapted screenplay for The Father, which he co-wrote with the film’s French director Florian Zeller.
British visual effects supervisor Andrew Lockley was part of the team who picked up won the award for best visual effects, for the film Tenet.
Completing the half-dozen British wins was composer Atticus Ross, who collected the award for best original score for the film Soul, along with Trent Reznor and Jon Batiste.
The most number of British wins at the Oscars since 2000 is nine, in 2009, the year of Slumdog Millionaire.
Oscars 2021: Full list of winners from the 93rd Academy Awards
Best picture: Nomadland
Best actor: Sir Anthony Hopkins (The Father)
Best supporting actor: Daniel Kaluuya (Judas And The Black Messiah)
Best actress: Frances McDormand (Nomadland)
Best supporting actress: Yuh-Jung Youn (Minari)
Best director: Chloe Zhao (Nomadland)
Best animated feature film: Soul
Best cinematography: Erik Messerschmidt (Mank)
Best film editing: Mikkel EG Nielsen (Sound Of Metal)
Best costume design: Ann Roth (Ma Rainey’s Black Bottom)
Best original score: Trent Reznor, Atticus Ross and Jon Batiste (Soul)
Best original song: Fight For You (Judas And The Black Messiah)
Adapted screenplay: The Father – Christopher Hampton and Florian Zeller
Original screenplay: Promising Young Woman – Emerald Fennell
Best production design: Mank
Best make-up and hairstyling: Ma Rainey’s Black Bottom
Best sound: Sound Of Metal
Best live-action short film: Two Distant Strangers
Best visual effects: Tenet
Best documentary feature: My Octopus Teacher
Best international feature: Another Round (Denmark)
Best animated short: If Anything Happens I Love You
Best documentary short: Colette
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