Accepting the prize on stage, Nolan, 54, thanked those who have “fought long and hard to reduce the number of nuclear weapons” in the world.
It was at last year’s Bafta that Navalny, which revolved around the late Russian opposition figure Alexei Navalny, won the same prize.
Murphy beat out The Holdovers star Paul Giamatti in what was considered a very tight race between the two actors.
Christopher Nolan’s epic atomic bomb picture Oppenhimer led the night with nominations in 13 categories – of which the film won seven, including Best Picture and Best Director.