Sir Alan’s works won a total of 19 BAFTAs, 10 Golden Globes and 10 Oscars during his career.
A statement sent on behalf of his family said he died on Friday morning.
Sir Alan is survived by his wife Lisa Moran-Parker, his children Lucy, Alexander, Jake, Nathan and Henry, and seven grandchildren.
Film director David Puttnam, who produced some of his films, was among those who paid tribute.
He said: “Alan was my oldest and closest friend, I was always in awe of his talent.
“My life and those of many others who loved and respected him will never be the same again.”