Robson was born in South Shields, County Durham, of Scottish descent to a family of six siblings. Many of her forebears were Engineers, mostly in shipping. Her father was a ship's Engineer who moved from Wallsend near Newcastle to Palmers Green in 1907 and Southgate in 1910, both in north London, and later to Welwyn Garden City.

Robson made her stage debut in 1921. By the 1930s she was appearing in several prominent films both in the UK and in Hollywood, alongside such stars as Laurence Olivier, Paul Muni and George Raft. Her most notable role was that of Queen Elizabeth I in both Fire Over England (1937) and The Sea Hawk (1940). In 1934, Robson played the Empress Elizabeth in Alexander Korda's Catherine the Great (1934). She was nominated for the Academy Award for Best Supporting Actress for her role as Angelique Buiton, a servant, in Saratoga Trunk (1945). The same year, audiences in the U.K. and the U.S. watched her hypnotic performance as Ftatateeta, the nursemaid and royal confidante and murderess-upon-command to Vivien Leigh's Queen Cleopatra in the screen adaptation of George Bernard Shaw's Caesar and Cleopatra (1945).

A plaque at 40 Handside Lane in Welwyn Garden City records Flora Robson living there from 1923 to 1925.

In 1931, she was cast as the adulterous Abbie in Eugene O'Neill's Desire Under the Elms. Her brief, shocking appearance as the doomed prostitute in James Bridie's play The Anatomist put her firmly on the road to success. "If you are not moved by this girl's performance, then you are immovable" the Observer critic wrote. This success would lead to her famous 1933 season as leading lady at the Old Vic.

She was nominated for an Academy Award for Best Supporting Actress as Angelique Buiton, a Haitian maid, in Saratoga Trunk (1945).

After the Second World War, demonstrating her range, she appeared in Holiday Camp (1947), the first of a series of films which featured the very ordinary Huggett family; as Sister Philippa in Black Narcissus (1947); as a magistrate in Good-Time Girl (1948); as a prospective Labour MP in Frieda (1947); and in the costume melodrama Saraband for Dead Lovers (1948). Her other film roles included the Empress Dowager Cixi in 55 Days at Peking (1963), Miss Milchrest in Murder at the Gallop (1963), the Queen of Hearts in Alice's Adventures in Wonderland (1972), and Livia in the aborted I, Claudius in 1937.

She was created a Commander of the Order of the British Empire (CBE) in the 1952 New Year Honours, and raised to Dame Commander (DBE) in the 1960 Birthday Honours. She was also the first famous name to become President of the Brighton Little Theatre.

On 4 July 1958, she received an honorary DLitt from Durham University at a congregation in Durham Castle.

She continued her acting career late into life, though not on the West End stage, from which she retired at the age of 67, often for American television films, including a lavish production of A Tale of Two Cities (in which she played Miss Pross). She also performed for British television, including The Shrimp and the Anemone. In the 1960s, she continued to act in the West End, in Ring Round the Moon, The Importance of Being Earnest and Three Sisters, among others.

She was the subject of This Is Your Life in February 1961 when she was surprised by Eamonn Andrews in central London.

Dame Flora Robson Avenue, built in 1962, in Simonside, South Shields, is named after her. There is a plaque on the house in Wykeham Terrace, Dyke Road, Brighton, and also one in the doorway of St. Nicholas's Church, of which Flora Robson was a great supporter.

She continued to act on film and television. She was last briefly seen as a Stygian Witch in the fantasy adventure Clash of the Titans in 1981. Both the BBC and ITV made special programs to celebrate her 80th birthday in 1982, and the BBC ran a short season of her best films.

She died in Brighton, aged 82; the cause was never revealed. She had never been married or had any children. The two sisters, with whom she shared her life and home, died around the same time: Shela shortly before Flora, in 1984, and Margaret on 1 February 1985.

In 1996, the British Film Institute erected a plaque at number 14 Marine Gardens, location of Flora's other home in Brighton, where she lived from 1961 to 1976.

A blue plaque sponsored by Southgate District Civic Trust and Robson's former school Palmers Green High School was unveiled at her family home from 1910 to 1921, The Lawe, 65, The Mall, Southgate, on 25 April 2010.