At a glittering ceremony here Sunday night, the British royal drama, which is about a stammering monarch, took away the awards for best film, outstanding British film, original screenplay, best actor (Colin Firth), best supporting actor (Geoffrey Rush), best supporting actress (Helena Bonham Carter), and best original music (Alexandre Desplat).
The film had received 14 nominations.
Rahman, who won a BAFTA in 2009 for his work in "Slumdog Millionaire", can now pin his hopes only on the penultimate - the Oscars. He has been nominated in two categories - original score and original song at the 83rd Annual Academy Awards for the original score in "127 Hours" as well as original song "If I Rise" for the same movie.
Christopher Nolan's "Inception" and David Fincher's "The Social Network" had a tie with three awards each.
While "Inception" got the gong for best visual effects, best sound and best production design, "The Social Network" bagged trophies in the best director, best adapted screenplay and best editing categories.
The best actress award was claimed by Natalie Portman for "Black Swan".
A special award for outstanding British contribution to cinema was given to the famous "Harry Potter" franchise.
"Toy Story 3" took away the award for the best animated film, beating "Despicable Me" and "How To Train Your Dragon".