The movie is a thriller-cum-melodrama about the unlikely relationship between a bare-knuckle boxer (Matthias Schoenaerts) and a whale trainer, played by Academy Award winner Marion Cotillard, who suffers a tragic workplace accident.
The president of the award jury, British playwright David Hare, praised it as "a film full of heart, violence and love."
French filmmaker Audiard won the same award at the London festival in 2009 for his prison drama "A Prophet."
American director Benh Zeitlin took the best debut feature prize with his atmospheric bayou saga "Beasts of the Southern Wild." Juror Hannah McGill praised the "daringly vast, richly detailed" film, which has won wide praise since its Sundance Film Festival debut earlier this year.
The trophy for best British newcomer went to Sally El Hosaini for "My Brother the Devil," the story of British-Egyptian brothers struggling with conflicting loyalties and identities in modern-day London. The best documentary prize went to Alex Gibney's "Mea Maxima Culpa: Silence in the House of God," an investigation of sexual abuse within the Roman Catholic church.
Director Tim Burton and actress Helena Bonham Carter - real-life partners as well as creative collaborators - received career honors known as British Film Institute Fellowships during an awards ceremony at London's Banqueting House.
Founded in 1957 to show the best of the world's cinema to a British audience, the London festival has in recent years tried to carve out a place on the international movie calendar with bigger pictures, more glittering stars and more high-profile awards.
Highlights 12-day festival included Ben Affleck's Iran hostage drama "Argo," Michael Haneke's Cannes Palme d'Or winner "Amour," Rolling Stones documentary "Crossfire Hurricane" and Roger Michell's "Hyde Park on Hudson," a comedy-drama with Bill Murray as U.S. President Franklin D. Roosevelt.
The festival wraps up Sunday with a gala screening of Mike Newell's adaptation of Charles Dickens' "Great Expectations," starring Bonham Carter and Ralph Fiennes.
(Copyright 2012 by The Associated Press. All Rights Reserved.)