Varma is the only child of an Indian father and a Swiss mother who was part Genoese Italian. She was a member of Musical Youth Theatre Company. She graduated from the Royal Academy of Dramatic Art (RADA) in London in 1995.
She is best known for her role as Niobe of the Voreni in HBO's Rome, which also starred Game of Thrones cast members Ciaran Hinds and Tobias Menzies. She is also known for her roles in the films Kama Sutra: A Tale of Love, Bride and Prejudice and Basic Instinct 2 and the TV series Luther and Human Target.