Syms started as a starlet. In her second film My Teenage Daughter (1954), she played Anna Neagle's "problem" daughter, and by 1960 had worked with Flora Robson, Orson Welles, Stanley Holloway, Lilli Palmer and William Holden — and made the film Ice-Cold in Alex (1958). Co-starring John Mills, Anthony Quayle and Harry Andrews, this has become a cult film in recent years because an extract from it was used in a beer commercial. It is an entertaining story about three British Army personnel and one German trying to get through enemy territory. A love scene between Mills and Syms was dropped from the film because it was considered too strong.
Also in 1958, she appeared in the English Civil War story The Moonraker with George Baker as her male lead. Syms played Tony Hancock's wife in The Punch and Judy Man (1962) along with her nephew, Nick Webb. Other comedies followed, such as The Big Job (1965) with Hancock's former co-star Sid James, but it was for drama that she won acclaim, including The Tamarind Seed (1974) with Julie Andrews and Omar Sharif, for which she was nominated for a British Film Academy award. My Good Woman in 1972 was a husband-and-wife television comedy series which ran until 1974 with Leslie Crowther. At the same time, she was one of two team captains on the BBC's weekly "Movie Quiz", hosted by Robin Ray. In 1975, she was the head of the jury at the 25th Berlin International Film Festival.
Shortly after the downfall of British Prime Minister Margaret Thatcher, Syms portrayed Thatcher in a TV play covering the events surrounding her demise on ITV, later recreating the role on the stage. In 1989, she appeared in the Doctor Who story Ghost Light.
From 2000 until 2003, Syms played the part of Marion Riley in the ITV comedy-drama series At Home with the Braithwaites.
In 2002, she starred in the serial, The Jury, and contributed "Sonnet 142" to the compilation album, When Love Speaks (EMI Classics). In 2006, she co-starred as Queen Elizabeth the Queen Mother in Stephen Frears' The Queen, alongside Oscar-winner Dame Helen Mirren. She also appeared in The Poseidon Adventure, an American television movie with little connection to the original movie of the same name made in the 1970s. She has also taken up producing and directing.
Among the many other famous actors and actresses Syms has worked with are: Dirk Bogarde, Marius Goring, Hardy Krüger, Herbert Lom, Cliff Richard, Jenny Agutter, Sophia Loren, George Peppard, Roger Moore, Ray Milland, Bernard Miles and Richard Todd.