His publisher Novello & Co. said in a statement Friday that Bennett died on Dec. 24 following a brief illness.
Bennett was nominated for Oscars for the scores for "Far from the Madding Crowd" in 1967, "Nicholas and Alexandra" in 1971 and "Murder on the Orient Express" in 1974.
A student of Pierre Boulez in 1957-58, Bennett's work evolved from the avant-garde to a more tonal style. As a pianist, he performed with singer Claire Martin and he recorded music by George Gershwin, Jerome Kern and Harold Arlen.
Bennett's extensive output included more than 200 works for the concert hall and 50 scores for film and television, five operas and miscellaneous works including settings of Christmas carols.
"Richard was the most complete musician of his generation -- lavishly gifted as a composer, performer and entertainer in a multiplicity of styles and genres," said Chris Butler, head of publishing for the Music Sales Group in London.
"He was a loyal friend to music, musicians, and music publishing and we will remember him with great respect and affection."
British composer Daryl Runswick said he had benefited from Bennett's help and encouragement.
"He was a cultured gay man and every aspect of his creativity was defined by elegance," Runswick wrote on The Guardian's website.
"He wanted, and achieved, a refined style in both his music and his life: that is why he went to New York, and was so happy there."
Bennett was born March 29, 1936, in Broadstairs near the English Channel coast, but his family moved to the safer area of Devon after war broke out. His mother, who had studied with the composer Gustav Holst and had sung in the first performance of "The Planets," was an early musical influence on her son.
"People ask what was the first piece of music I wrote. There was no first piece," Bennett said in an interview last year with The Guardian newspaper.
"I just scribbled away and eventually a C-major chord was there. I didn't ever decide I was going to be a composer. It was like being tall. It's what I was. It's what I did."
He moved to New York in 1979, following the end of a long relationship and feeling stifled in Britain. Stephen Sondheim and Leonard Bernstein supported his application for a green card work permit.
"I was doing a lot of things out of guilt," he said of his departure from Britain.
"I hated teaching composition. I was playing music I didn't particularly want to play, being on committees I didn't want to be on. I wanted to write music, and cook, and play cards, and have a nice time," The Guardian quoted him as saying.
In New York he indulged his passion for jazz, accompanying singer Claire Martin in shows at the Algonquin Hotel and drawing praise from The New York Times as "a sensitive, truly intimate collaborator."
He helped Paul McCartney with his orchestral work "Standing Stone," commenting on sections faxed by the former Beatle.
"I sent him one, thinking it was pretty good," McCartney said. "A few minutes later, I got a fax back with the word `feeble' scribbled across it.
"I phoned him straight back and said, `Richard, that's what my teacher wrote on my essays. You're a sensitive artist, and if you don't like something, could you please write, `That's a little below par?"'
Bennett coached Elizabeth Taylor to sing a nursery rhyme for the film "Secret Ceremony," for which he wrote the musical score. Prince Charles commissioned Bennett in 2005 to write "Reflection on a Scottish Folk Song" in honor of the prince's grandmother, Queen Mother Elizabeth.
Bennett was knighted in 1998. Funeral details were not announced.