Soon after Gillian's birth, her family moved to Puerto Rico for 15 months; she then lived for five years in Roseberry Gardens, London N4, and finally for 15 months in Albany Road, London N4, so that her father could attend the London Film School. When Anderson was 11 years old, her family moved again, this time to Grand Rapids, Michigan. With her English accent and background, Anderson was mocked and felt out of place in the American Midwest and soon adopted a Midwest accent. To this day, her accent depends on her location — for instance, in an interview with Jay Leno she spoke in an American accent, but shifted it for an interview with Michael Parkinson.
Gillian attended a program for gifted students with a strong emphasis on the humanities. She had her nose pierced in the early 1980s and dyed her hair various colors. Her high school classmates voted her as "Most Bizarre," "Class Clown", "Most Likely to go Bald" and "Most Likely to be Arrested." Fulfilling the last of these predictions, she was caught trying to jam the high school doors by filling their locks with glue on the eve of her graduation, for which she was arrested.
Anderson was interested in marine biology, but began acting her freshman year in high school productions, and later in community theater, and served as a student intern at the Grand Rapids Civic Theatre & School of Theatre Arts. She attended The Theatre School at DePaul University in Chicago (formerly the Goodman School of Drama), where she earned a Bachelor of Fine Arts in 1990. She also participated in the National Theatre of Great Britain's summer program at Cornell University.
- In 2003, she won the Whatsonstage.com Theatregoers' Choice Best Actress Award for her West End debut in Michael Weller's two-hander "What the Night Is For". The following year, she starred in Rebecca Gilman's play "The Sweetest Swing in Baseball" which ran at London's Royal Court Theatre from March 25 through May 15, 2004. From May 14 through July 18, 2009, she played Nora in a new version of Ibsen's "A Doll's House" at the Donmar Warehouse in London. She received a Laurence Olivier Nomination for her performance.