Richardson was born in Cheltenham, and when he was a baby his mother, Lydia Russell, left his father and took him with her to Gloucester, where she raised him a Roman Catholic (his father and brothers were Quakers). His father supported them with a small allowance. Lydia Richardson wished Ralph to become a priest. Ralph was an altar boy in Brighton, England, and was educated by the Xaverian Brothers, but he did not become a priest, nor was he ever particularly religious.

He made his West End début in 1926. Thereafter he became one of the Old Vic's major stars. In 1933 he played the title role in W. Somerset Maugham's final play Sheppey at Wyndham's Theatre. After World War II, he became co-director of the Vic, and also appeared with the Royal Shakespeare Company in Stratford-on-Avon.

From 1954 - 1955 he played the character of Dr. John Watson (mistakenly called 'James' in several episodes) in an American/BBC radio co-production of canonical Sherlock Holmes stories, which starred John Gielgud as the famous consulting detective.

His film appearances included The Heiress, Richard III (playing Buckingham to Laurence Olivier's Richard), O Lucky Man!, Oh! What a Lovely War, Dragonslayer, and Time Bandits. His career has often been compared with that of Olivier, Alec Guinness and John Gielgud.

Richardson was knighted by King George VI in 1947. His final film appearance was as the sixth Earl of Greystoke in the 1983 movie Greystoke - The Legend of Tarzan, Lord of the Apes, for which he was again nominated for an Academy Award. He also won the BAFTA Award for Best British Actor for The Sound Barrier (1952), and was nominated on another three occasions.

In 1963 he won the Best Actor Award at the Cannes Film Festival for Long Day's Journey Into Night. He was also nominated for three Tony Awards for his work on the New York stage.

Sir Ralph died of a stroke, aged 80, and was interred at Highgate Cemetery.

He was a nephew of the mathematician Lewis Fry Richardson.