Sprigg's roles with the Royal Shakespeare Company included Nurse in Romeo and Juliet, Gertrude in Hamlet and Beatrice in Much Ado About Nothing. In 1978, she won the Olivier Award for Best Supporting Actress for Arnold Wesker's Love Letters on Blue Paper. She received a BAFTA nomination for Best Supporting Actress for the 1995 film Sense and Sensibility. Her other films included Richard's Things (1980), Impromptu (1991), Paradise Road (1997) and Harry Potter and the Philosopher's Stone (2001).
Spriggs died on 2 July 2008 aged 78. Her funeral service and interment took place at Saint Mary the Virgin's Churchyard in Thame, Oxfordshire. It was attended by family and friends, including her daughter, Sinéad Cusack, James Ellis and Lesley Sharp. Her funeral was also attended by Jeremy Irons, Robert Hardy, and Peter Vaughan, who all paid tribute to their friend and fellow actor.