As an actress, Hampshire worked in the theatre before moving to film and television work. She took the title role in a dramatised version of Little Black Sambo recorded by HMV Junior Record Club (words by David Croft, music by Cyril Ornadel). and sang on The Midday Show when ITV Anglia began broadcasting (as Anglia Television) in 1959. Her first starring role was in the film During One Night in 1960. She then took the leading role in a 1962 BBC adaptation of What Katy Did. Soon afterwards, she was taken up by Walt Disney and starred in The Three Lives of Thomasina (opposite Patrick McGoohan) and The Fighting Prince of Donegal. She would later appear opposite McGoohan again, in two episodes of Danger Man. She co-starred with Cliff Richard in Sidney J. Furie’s 1964 musical Wonderful Life.

In 1966, she was introduced to American TV viewers in the pilot episode of The Time Tunnel as a young passenger on the Titanic who befriends Dr Tony Newman. She later portrayed conservationist Joy Adamson in Living Free, the sequel to Born Free. In 1972, she played three different characters in Malpertuis, directed by Harry Kumel. She is known for her work on television, appearing in several popular television serials, including The Andromeda Breakthrough (1962) in which she replaced Julie Christie who was not available for the show but had played the part of Andromeda in the first season of A for Andromeda (1961). Her most notable television role in the 1960s came in the BBC’s 1967 adaptation of The Forsyte Saga, in which she played Fleur.

Hampshire received Emmy Awards from the Academy of Television Arts & Sciences for her roles in The Forsyte Saga (1970), The First Churchills (1971) and Vanity Fair (1973). In 1973 she appeared again on US television with Kirk Douglas in a musical version of Dr. Jekyll and Mr. Hyde. Other miniseries in which she appeared are The Pallisers, The Barchester Chronicles and Coming Home. She was the subject of This Is Your Life in 1992 when she was surprised by Michael Aspel at the Ritz Hotel. In 1997 she appeared in the ITV television series The Grand where she played a madame residing in the hotel. More recent TV roles include Molly MacDonald, Lady of Glenbogle, in Monarch of the Glen (2000–05) / and an appearance in Casualty (Series 26, No Goodbyes, 19 November 2011) as Caitlin Northwick (alongside Michael Jayston).

Until the publication in 1981 of her autobiography, Susan’s Story, few people were aware of her struggle with dyslexia. Since then she has become a prominent campaigner in the UK on dyslexia issues and was president of the Dyslexia Institute from 1995–1998.

Her second book, The Maternal Instinct (1984), discussed women and fertility issues and she published a collection of interviews, Every Letter Counts: Winning in Life Despite Dyslexia, in 1990. She has written children’s books, including Lucy Jane at the Ballet, Lucy Jane and the Russian Ballet, Lucy Jane and the Dancing Competition, Lucy Jane on Television, Bear’s Christmas, Rosie’s First Ballet Lesson and Rosie’s Ballet Slippers as well as various books and videos about her lifelong hobby of gardening, including Easy Gardening, My Secret Garden and Trouble Free Gardening.

Hampshire was appointed Officer of the Order of the British Empire (OBE) in the 1995 Birthday Honours for services to dyslexic people. In the 2018 New Year Honours, she was made Commander of the Order of the British Empire (CBE) for services to drama and charity.

Hampshire has been active on the stage, taking the lead roles in many leading plays. In 2007, she was in the play The Bargain, based on a meeting between Robert Maxwell and Mother Teresa. She played the Fairy Godmother in pantomime at the New Wimbledon Theatre in 2005–06 and at the New Victoria Theatre in Woking in 2006–07. In 2008, she joined the relatively small band of actors who have played two generations in the same play on different occasions. Her appearance at the Chichester Festival Theatre in Somerset Maugham’s The Circle as Lady Catherine Champion-Cheney in 2008 followed on from her appearance in the same play (and venue) as Elizabeth Champion-Cheney (Lady Catherine’s daughter-in-law) in 1976.