Bron was born in Stanmore, London into a Jewish family; her father who was of eastern european descent , shortened the surname to "Bron" from "Bronstein" when founding Bron's Orchestral Service. She was educated at the North London Collegiate School and Newnham College, Cambridge.

Bron was the partner of the architect Cedric Price until his death in 2003. They had no children. Her elder brother is the record producer Gerry Bron.

Bron began her career in the Cambridge Footlights revue of 1959, entitled The Last Laugh, in which Peter Cook also appeared. The addition of a female performer to the Footlights was a departure, having been until that point all-male, with female characters portrayed in drag. As with many others of the British satire boom, participation in the Footlights was a springboard to a long career in British comedy as both a writer and performer.

Her film appearances include the role of Ahme in the Beatles film, Help! (her given name inspired Paul McCartney while composing "Eleanor Rigby"). Other roles included the doctor who grounds the Lothario played by Michael Caine in Alfie, the unattainable Margaret Spencer in Peter Cook and Dudley Moore's film Bedazzled, and Hermione Roddice in Ken Russell's Women in Love. She appears in the film Two for the Road alongside Albert Finney, Audrey Hepburn and William Daniels. More recently she has appeared in the film adaptations of A Little Princess, The House of Mirth, Black Beauty and in Wimbledon.

Eleanor Bron's earliest work for television included appearances on Not So Much a Programme More a Way of Life, My Father Knew Lloyd George and BBC-3, where she performed in sketches with John Fortune; they had already worked together at Peter Cook's Establishment Club. Later, her work included such programmes as Where Was Spring? (1969) and After That, This (1975) – the one with the "egg" timer in the opening credits.

She collaborated with novelist and playwright Michael Frayn on the BBC programmes Beyond a Joke (1972) and Making Faces (1975).

She appeared in a 1982 episode ("Equal Opportunities") of the BBC series Yes Minister, playing a senior civil servant in Jim Hacker's Department. Hacker plans to promote her to strike a blow for equal opportunities.

Bron appeared in a brief scene in the BBC science fiction television series Doctor Who serial City of Death alongside John Cleese as art critics in Denise Rene's art gallery in Paris. The pair are admiring the TARDIS, thinking it to be a piece of art, when the Doctor (Tom Baker), Romana (Lalla Ward) and Duggan (Tom Chadbon) rush into it and it dematerialises. Bron's character, believing this to be part of the work, states that it is "Exquisite, absolutely exquisite!"

She also appeared as an art critic in a parody of an Andy Warhol documentary on the BBC sketch comedy show French and Saunders.

Later, she had a more substantial guest role in another Doctor Who television serial, 1985's Revelation of the Daleks. She has more recently also appeared in an audio drama based on Doctor Who by Big Finish Productions, (Loups-Garoux), in which she plays the part of wealthy heiress Ileana de Santos.