The three-hour epic about the making of the atomic bomb also won awards for leading actor Cillian Murphy, who portrays American theoretical physicist J. Robert Oppenheimer as well as supporting actor Robert Downey Jr, editing, cinematography and original score.
Christopher Nolan, who took home his first BAFTA for directing, used his time on stage to talk about nuclear proliferation.
"But in the real world there are all kinds of individuals and organizations who have fought long and hard to reduce the number of nuclear weapons in the world. Since its peak in 1967 they've done it by almost 90%. Of late, that's gone the wrong way and so, in accepting this I do just want to acknowledge their efforts and point out that they should the necessity and the potential of efforts for peace."
Another standout this year was the sex-charged Gothic comedy 'Poor Things', winning five prizes overall including the award for leading actress Emma Stone.
Da'Vine Joy Randolph won the supporting actress prize for her role in "The Holdovers," a comedy set in a boys' boarding school.
"There have been countless Marys throughout history who have never got a chance to wear a beautiful gown and stand on this stage, here in London. Telling her story is a responsibility that I do not take lightly, and this award is a beautiful reminder of how her story has rippled through the world. Thank you so much. Thank you."
The BAFTAs have kept up "Oppenheimer'"s domination of awards season this year.
It swept the Golden Globes with five wins in January and leads nominations for the Academy Awards next month.
