In a star-studded ceremony, Kate Winslet also picked up the BAFTA for leading actress for her role as a former Nazi prison camp guard in "The Reader", while Mickey Rourke took the leading actor gong for "The Wrestler".
"Slumdog Millionaire" had been nominated for 11 awards and took home seven, including best director for Danny Boyle, best adapted screenplay for Simon Beaufoy and the music, cinematography, editing and sound prizes.
Made by a British team but with an Indian cast and crew, the movie is a favourite to win best film at the Oscars on February 22.
Producer Christian Colson said he would like to share the best film award with the people of Mumbai, saying: "Our amazing cast and crew in Mumbai realised the dream, with their blood and sweat and tears and love."
Before the ceremony, fans braved the rain outside the Royal Opera House in London's Covent Garden, jostling for a chance at an autograph from one of the A-listers present, including Brad Pitt, Angelina Jolie and Robert Downey Jr.
"Slumdog Millionaire" actor Dev Patel seemed as star-struck as anyone -- he was nominated for leading actor but said he never expected to win, and the main thing he wanted from the night was to meet Pitt.
"I'm 18 years old and I'm at the BAFTAs!" said Patel, who still lives with his parents and sister in Harrow, north-west London.
Winslet beat rivals Jolie, Kristin Scott Thomas and Meryl Streep to take the second BAFTA of her career -- she won best supporting actress in 1995 -- and her second award for "The Reader" after a Golden Globe last month.
She will be up against Streep and Jolie again at the Oscars.
"I want to share this with two producers on this film -- I know I'm not alone when I say I can't believe they're no longer with us, Anthony Minghella and Sydney Pollack," the 33-year-old said in her acceptance speech.
Rourke's win secures his comeback after years in the wilderness, and in his speech he thanked "The Wrestler" director Darren Aronofsky who "gave me a second chance after fucking up my career for 15 years".
Heath Ledger, who was found dead in his New York apartment a year ago, was awarded with a posthumous BAFTA for best supporting actor for his menacing performance as the Joker in the latest Batman movie, "The Dark Knight".
Terry Gilliam directed the last film Ledger worked on, and in accepting the award of BAFTA fellowship, paid tribute to the 28-year-old.
"It would have been nice if Heath had won more awards when he was alive," he said, referring to Ledger's posthumous Golden Globe and recent Oscar nomination for his role in "The Dark Knight". "He was a genius."
Penelope Cruz won best supporting actress for her role in Woody Allen's sparky romantic drama, "Vicky Cristina Barcelona", an honour she said came as a complete shock. "I'm so happy, so excited, so surprised," she said.
"The Curious Case of Benjamin Button," starring Pitt as a man who ages in reverse, was nominated for 11 awards but had to make do with just three -- best production design, make up and hair, and special visual effects.
"Man on Wire", James Marsh's documentary about Frenchman Philippe Petit's daring high-wire walk between the twin towers in New York in August 1974, won the BAFTA for outstanding British film.
Black comedy "In Bruges" won best original screenplay, while "I've Loved You So Long" was awarded the prize for best non-English language film.
The BAFTAs have grown in prominence in recent years and are now seen as one indicator of who will win the film industry's biggest gongs, the Oscars.
Last year, the winners of BAFTA's four acting categories went on to win the equivalent Academy Awards -- although "Atonement" won best film here only to lose out to "No Country for Old Men" in Hollywood.