Bryan was born as Dora Mary Broadbent in Southport, Lancashire, England, and was recognised for her distinctive speaking voice, which became a trademark of her performances. Her father was a salesman and she attended Hathershaw County Primary School in Oldham, Lancashire. Her career began in pantomime before World War II, during which she joined the ENSA in Italy to entertain British troops.

She became a regular performer in the West End of London after the war, where she became a star of theatrical revues. She soon followed many of her theatre contemporaries by moving into film acting, generally playing supporting roles. She often played women of easy virtue — for example in Ealing's The Blue Lamp (1950) and The Fallen Idol (1948), one of her earliest films. She appeared in similarly stereotypical female roles in other films, for example The Cockleshell Heroes (1955), Carry On Sergeant (1958) and The Green Man (1956).

In 1961, she appeared in A Taste of Honey. The film won four BAFTA awards: Director Tony Richardson won Best British Screenplay (with Shelagh Delaney) and Best British Film, while Bryan won Best Actress and co-star Rita Tushingham was named Most Promising Newcomer. In 1963 she recorded the Christmas song 'All I want for Christmas is a Beatle'. She played a head mistress in The Great St Trinian's Train Robbery (1966). She appeared in a cameo role in 1955 on the BBC radio series Hancock's Half Hour, episode now known as "Cinderella Hancock".

Bryan appeared in the Anglo-Argentine Hitchcockian thriller, Apartment Zero. The film was featured in the 1988 Sundance Film Festival and was directed by Martin Donovan (the Argentine aka: Carlos Enrique Varela y Peralta-Ramos) and starred Hart Bochner and Colin Firth. Bryan plays the role of one of two eccentric characters (the other was played by Liz Smith) described by the Washington Post as two "... tea-and-crumpet gargoyle-featured spinsters who snoop the corridors."

In 2000 she joined the cast of the long-running BBC comedy series Last of the Summer Wine as Aunt Roz Utterthwaite; she left the show in 2005 to concentrate on stage work in theatre, though she has not been written out. Her last film appearance was in Gone to the Dogs (2006) opposite Anthony Booth.

She was also frequently a guest star on Absolutely Fabulous as June Whitfield's on-screen friend Dolly (originally called Milly). She received a BAFTA nomination in 2002 for this role. In September 2006, she was due to tour in the comedy There's No Place Like a Home but withdrew early in the tour because of her husband's continued ill health.

Her autobiography According To Dora was published in 1987 and has since been updated and republished. In 1996, she was awarded the OBE in recognition of her services to acting and she was awarded a Laurence Olivier Award in 1996 for her role in the West End production of the Harold Pinter play, The Birthday Party.

She was married to former Lancashire County Cricketer Bill Lawton until his death as a result of Alzheimer's disease in August 2008. The couple met in Oldham during World War II and were married at Werneth St Thomas, Oldham in 1954. During his final years she reduced her public commitments to enable herself to look after him, as well as suffering with health problems herself, including a serious operation for a hernia.

She once owned Clarges Hotel on the Brighton seafront, which was used as an exterior location in the films Carry On Girls and Carry On at Your Convenience. She and her husband were forced to sell the bulk of the building as a result of bankruptcy, but they retained a flat with a sea view on the first floor for many years. The old Clarges hotel can be found at 115–119 Marine Parade. Still maintaining its original structure, the rooms of the hotel have been reconverted into flats, which are rented and owned by local Brighton residents.

In 2005 Bryan had to leave Last Of The Summer Wine, reportedly because of her forgetfulness and inability to remember her lines.