After beginning her career in British films in the 1930s, she would later transition to major Hollywood productions, earning a Golden Globe Award nomination for her performance in But Not for Me (1959).

Other notable roles include in the comedy The Pleasure of His Company (1961), the Spanish horror film The House That Screamed (1969), and in the miniseries Peter the Great (1986), which earned her another Golden Globe Award nomination.

Palmer, who took her surname from an English actress she admired, was one of three daughters born to Alfred Peiser [de], a German Jewish surgeon, and Rose Lißmann (or Lissmann), a German Jewish stage actress in Posen, Germany (today Poznań, Poland).

While performing in cabarets, she attracted the attention of British talent scouts and was offered a contract by the Gaumont Film Company.

They also appeared in the 1951 British melodrama The Long Dark Hall, and later starred in the film version of The Four Poster (1952), which was based on the award-winning Broadway play of the same name, written by Jan de Hartog.

On the small screen, in 1974 she starred as Manouche Roget in the six-part television drama series The Zoo Gang, about a group of former underground freedom fighters from the Second World War, with Brian Keith, Sir John Mills and Barry Morse.

Palmer was married to Argentine actor Carlos Thompson from 1957 until her death in Los Angeles from abdominal cancer[12] in 1986 at the age of 71.