He made his film debut in 1953 with The Cruel Sea and went on to make about 30 films. He also performed with the Royal Shakespeare Company in leading roles such as King Lear and Malvolio in Twelfth Night.
He made his name on stage as a Shakespearean actor and appeared in more than 70 film and TV productions. He had been suffering from prostate cancer for several years, and died of the disease at his home in Kent. The Society of London Theatre has announced that the West End will dim its lights at 19:00 BST in the actor's memory. Sir Donald's family described his death as a "huge loss" and asked for their privacy to be respected.
He was appointed a CBE in 1979 and then knighted in 1997 for his services to drama. Although renowned for his theatre work, he was arguably best known to the masses for his TV appearances - in the sitcom Never the Twain and the BBC legal drama Judge John Deed.
His son, actor Marc Sinden, said that his career was "probably unique in our business". According to Marc Sinden, Sir Donald was the last person living to have known Oscar Wilde's lover Lord Alfred Douglas and was one of only two people to attend his funeral.