first film appearance was in the movie The Woman in the Hall. She decided to become an actress as a child and worked in a theatre before moving on to film and television work. During this period she took the title role of a dramatised version of Little Black Sambo recorded by HMV Junior Record Club (words by David Croft, music by Cyril Ornadel). 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.
In 1966, she was introduced to American TV viewers in the pilot episode of The Time Tunnel, guest starring as a young passenger of the ill-fated Titanic that befriends Dr. Tony Neuman after he appears on the ship. Later, she portrayed conservationist Joy Adamson in Living Free, the sequel to Born Free. Also in 1972, she played three different characters in Malpertuis, directed by Harry Kumel.
Hampshire is well known for her work on television. She appeared in several popular television serials, notably in the BBC's blockbuster, The Forsyte Saga (1967), in which she played Fleur and the series 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 A for Andromeda (1961). The popularity of this series was a factor in the creation of the PBS program Masterpiece Theatre (the first series aired was The First Churchills in which she played Sarah Churchill). 1973 saw Hampshire again on US television with Kirk Douglas in a musical version of Dr. Jekyll and Mr. Hyde. More recent TV roles include Molly Macdonald 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).
She 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). Other miniseries in which she appeared are The Pallisers, The Barchester Chronicles, and Coming Home.