Goring was born in Newport, Isle of Wight, England, the son of Dr Charles Goring and Kate Macdonald. After attending the Perse School in Cambridge, where he became a friend of an older boy, the Future documentary film maker Humphrey Jennings, he studied at the universities of Frankfurt, Munich, Vienna and Paris. He first performed professionally in 1927. His early stage career included appearances at the Old Vic, Sadler's Wells, Stratford and several European tours; he was fluent in French and German. He first worked in the West End in a 1934 revival of Granville-Barker's The Voysey Inheritance at the Shaftesbury Theatre. During the 1930s, he played a variety of Shakespearean roles, including Feste in Twelfth Night (1937), Macbeth and Romeo, in addition to Trip in Sheridan's The School for Scandal. In 1929, he became a founding member of British Equity, the actors' union, and became its President from 1963 to 1965, and again from 1975 to 1982. Goring's relationship with his union was fraught with conflict: he took it to litigation on three occasions. In 1992 he unsuccessfully sought to end the block on the sale of radio and television programmes to (the still) apartheid South Africa.
During World War II he joined the army, becoming supervisor of BBC radio productions broadcasting to Germany and continued to act under the name Charles Richardson, because of the association of his name with Hermann Göring. In 1941, he married his second wife, the Actress Lucie Mannheim, who worked with him in The Adventures of the Scarlet Pimpernel. She died in 1976, and the next year Goring married television Producer Prudence Fitzgerald, who survived him.
His TV work included starring as Sir Percy Blakeney in The Adventures of the Scarlet Pimpernel (ITV, 1955) (a role which he also had in the 1952-53 radio show), a series which he also co-wrote and produced; Theodore Maxtible in the Doctor Who story The Evil of the Daleks (BBC, 1967); title role in The Expert (BBC, 1968–1976); Paul von Hindenburg in Fall of Eagles (BBC 1974). King George V in Edward & Mrs. Simpson (Thames, 1980); and The Old Men at the Zoo (BBC, 1983).
He was made a Fellow of the Royal Society of Literature in 1979 and appointed Commander of the Order of the British Empire (CBE) in 1991. He died from cancer in 1998 aged 86.
