Mills, who won an Oscar for his role in "Ryan's Daughter," died peacefully Sunday, a family spokesman said in a statement.
Mills made his stage debut in 1929 as a chorus boy, and went on to a career that spanned 73 years. He performed in many World War II British patriotic films, having been released from military service himself in 1941 due to an ulcer.
Despite suffering deafness and near blindness, he continued working, last playing a coke-snorting cameo role in 2003's "Bright Young Things," and performing at a 100th birthday pageant for the Queen Mother.
Mills is survived by his wife, playwright Mary Hayley Bell, his son, Jonathan, and daughters Juliette and Hayley, both actors.