The Oscar-winning director died on Sunday.
BAFTA has described its former president as a "titan of British cinema" who set an example of "industry, skill and compassion" that business would do well to live up to.
In a statement the film academy added: "We are deeply saddened to learn of the passing of esteemed filmmaker and former BAFTA President, Lord Attenborough Kt, CBE, whose passionate support of BAFTA for more than 50 years was integral to who we are today. He will be sorely missed.
"A titan of British cinema, to say he embodied its finest qualities is to have it backwards. British film would do well to live up to the example of industry, skill and compassion set by Richard, Lord Attenborough."
BFI chief executive Amanda Nevill said: "The world has lost a very, very special person.
"Dickie was multi-talented as an actor, producer and world-class film director, but he was also a warm, compassionate and empathetic man, and a friend to all those who met him.
"He loved the art and culture of film and was a tremendous advocate for every part of it, not least for the BFI where he was chair for 13 years, as well as for the British film industry, playing a major part in enabling it to attain and hold the position it has today as a world leader.
"His support for individuals, whether they were starting out in the industry or accomplished professionals such as himself, knew no bounds and his legacy will continue to be an inspiration for generations to come. We are all saddened."
Meanwhile US actor Dylan McDermott, who starred alongside Attenborough in the 1994 reboot of Christmas film Miracle on 34th Street, paid tribute to the man who played Kris Kringle, writing on Twitter: "Rest in peace Richard Attenborough. U (sic) were the best Santa ever."
Their co-star and former child actress Mara Wilson also added: "Sir Richard Attenborough was the only Santa Claus I ever believed in. A wonderful man. Still in shock right now. May he rest in peace."
Hollywood actress Mia Farrow, who worked with Attenborough in 1964's Guns at Batasi, also added her own tribute to her friend, and wrote: "Richard Attenborough was the kindest man I have ever had the privilege of working with. A Prince. RIP 'Pa' - and thank you."
Attenborough starred in numerous hit movies including Jurassic Park and won eight Academy Awards for 1982 epic Gandhi, including best film and best director.
Born in Cambridge in August 1923, Attenborough demonstrated a love of the arts from a young age and won a scholarship to prestigious stage school RADA aged 17.
His career in movies would span over 50 years, a highlight being his 1982 film Gandhi which clinched eight Oscars, including best film and best director.
Top directors Satyajit Ray and Steven Spielberg to lured him out of self-imposed retirement to appear, respectively, The Chess Players in 1977 and the 1993 blockbuster Jurassic Park.
Away from films, he held numerous other positions, most notably chairman of Channel 4, from 1987 to 1993.
He appeared at the High Court to defend the broadcaster's decision not to name a source used in a documentary on Northern Ireland despite risking jail for contempt of court.
He was made a life peer in 1993.
Days away from his 91st birthday, Lord Attenborough had been wheelchair-bound since a fall in 2008. He and his wife lived in a residential home in Hertfordshire.
Lord Attenborough was the brother of Sir David Attenborough, the popular nature documentary-maker.