Affleck also won the best director trophy for "Argo", about the rescue of American hostages in Iran during the 1979 revolution, and the movie is now in pole position to win the biggest movie award of all on Oscar night.
"You are remarkable at what you do. You're smart and you know what you want but more importantly you love what you're doing," George Clooney, one of the film's producers, told Affleck on stage as they accepted the best film award.
Steven Spielberg's biopic of Abraham Lincoln was nominated in 10 categories but went away with just one award for Day-Lewis, following a pattern seen at the Golden Globes and at other prestigious U.S. award nights.
The reclusive Day-Lewis, a method actor well-known for staying in character during the entire filming period of his movies, began his victory speech by satirising his own working habits.
"Just on the chance that I might one day have to speak on an evening such as this, I've actually stayed in character as myself for the last 55 years," he said to laughs from the audience at the Royal Opera House.
"Every time I rise from a chair it spontaneously unleashes a soundtrack of thunderous applause, with a few boos and some drunken hecklers."
Emmanuelle Riva, an 85-year-old French actress, won the BAFTA for leading actress for her part as a retired music teacher struggling to cope with the aftermath of a stroke, in Austrian director Michael Haneke's "Amour".
The award finally brings a win for Riva who was nominated for a BAFTA in the foreign actress category in 1961 for "Hiroshima, Mon Amour", but lost out to Shirley MacLaine.
Haneke's harrowing French-language "Amour" also won the BAFTA for best film not in the English language.
Anne Hathaway won the BAFTA for best supporting actress for her singing role as the tragic Fantine in "Les Miserables", the movie version of a global hit stage musical.
"What am I thinking? I almost walked past George Clooney without hugging him. That's just stupid," she said after being presented with her statuette by the Hollywood heart-throb.
"I'm so relieved I'm coming down with laryngitis because the location, the giddiness, this could be a recipe for disaster," she said before launching into a breathless thank you speech.
Christoph Waltz won the supporting actor award for his performance in Quentin Tarantino's slavery-era Western "Django Unchained", which also won the best original screenplay BAFTA.
JOY FOR BOND FANS
The James Bond movie "Skyfall" beat "Les Miserables" to win the BAFTA award for outstanding British film, a rare joy for 007 fans who feel the Martini-loving spy has been long overdue for a major trophy.
Judi Dench, who plays spymaster M in "Skyfall", leapt out of her seat with a cry of surprise when the award was announced at the start of the night.
"We all had very high expectations for the film and I think it's fair to say all of them have been exceeded, and this really is the icing on the cake," said Sam Mendes, the film's director.
"Skyfall" has become the most successful film in British box office history, but ahead of the ceremony the odds had been on "Les Miserables" to win. The Bond franchise has a long history of awards disappointments.
"Skyfall" also took the award for original music, while "Les Miserables" took four BAFTAs. As well as Hathaway's prize, the musical won best production design, sound, and make-up and hair.
"Les Mis", as it is popularly known in Britain, has been a huge box office hit and fans sang songs from the film at Hugh Jackman, one of its stars, as he walked the red carpet in the rain just before the ceremony.
Ang Lee's "Life of Pi", about a man and a tiger lost at sea, won two BAFTAs, one for best cinematography and another for visual effects. The tiger, a central character, was entirely conjured out of special effects.
Versatile British director Alan Parker, whose body of work ranges from musical gangster film "Bugsy Malone" to Turkish-set prison thriller "Midnight Express" and civil rights drama "Mississippi Burning", received a BAFTA fellowship.
"It's a sign I'm getting old. Next it's a memorial service," Parker told Reuters on the red carpet.