Edinburgh-born, honey-blonde Hannah Gordon arrived on the screen in the mid-60s with a role in the first episode of the British horror/sci-fi anthology series Out of the Unknown (1965). In the course of the next five decades, Gordon became immensely popular with audiences in both serious and comedic roles on television, beginning with leads and later gracefully transitioning into supporting roles. She is quoted as saying "You have to look your age and deal with that".

Gordon's mother Hannah ((née Grant), died from a heart attack when she was nine. Her father, William Henry Gordon, suffered from advanced Parkinsons Disease and passed away three years later. Young Hannah came under the guardianship of an uncle who enrolled her in elocution classes. Living independently by the age of fourteen, she was able to determine her own career path which began with drama studies at the Royal Scottish Academy of Music and Drama in Glasgow. Following her graduation, Gordon had her first performing experience on the repertory stage in Dundee. In 1967, she appeared as Florence Crompton in the play Spring and Port Wine, a role she reprised for the film version three years later. Her first big hit on the screen was as Suzie Basset in the BBC1 sitcom My Wife Next Door (1972), co-starring alongside John Alderton. The storyline revolved around a divorced couple of city dwellers hoping to start new lives in the country, only to find themselves as neighbours in adjoining cottages. The show garnered a British Academy Television Award for Best Situation Comedy in 1973.

Gordon's next big role was as the elegant Lady Virginia Bellamy in the long running Edwardian drama series Upstairs, Downstairs (1971), her character in this being several years older than herself. Other performances in period garb have included Agnes Wickfield in David Copperfield (1966), the waif-like Biddy, snubbed by Pip in Great Expectations (1967) and the resourceful Mary Garth in Middlemarch (1968). She also played Ann Treves, wife of the prominent surgeon and anatomist Sir Frederick Treves, in David Lynch's acclaimed motion picture The Elephant Man (1980). Gordon commanded further leads in the banking dramas Telford's Change (1979) and Joint Account (1989), as well as in the (rather less successful) sitcom Goodbye, Mr. Kent (1982), opposite Richard Briers. She was featured several times as foil for the stars on The Morecambe & Wise Show (1978) and has made guest appearances in Doctor Who (1963), The Persuaders! (1971), Jonathan Creek (1997), Monarch of the Glen (2000) and (against type) as a sociopathic killer in Midsomer Murders (1997). Her character Glynis also killed off Victor Meldrew (a hit-and-run) in the final episode of One Foot in the Grave (1990). In the last episode of Hustle (2004)'s seventh season, she played an old paramour of 'roper' Albert Stroller (Robert Vaughn).

In the 70s and 80s, Gordon often featured as a panelist on the game show Call My Bluff (1965). Her face remained in the public eye with commercials for the Safeways supermarket chain and as presenter of the lifestyle television show Watercolour Challenge (1998) between 1998 and 2002. Her work on both the classical and contemporary stage has included Othello (as Desdemona, 1975), the title role in Shirley Valentine (1989) and Lady Chiltern in An Ideal Husband (1992-3).

Hannah Gordon's husband was the late London-born cinematographer Norman Warwick, who was twenty years her senior. They had first met during the filming of Spring and Port Wine (1970).