Buring was born 22 September 1979, in Sweden, as Anna Margaretha My Buring Rantapää, but grew up in the Middle East. When she turned 16, she moved to Great Britain. She attended secondary school at the American British Academy in Muscat, Oman, with her childhood friend Stegath Dorr, who is a character actor and a prolific horror filmmaker. Buring graduated from the London Academy of Music and Dramatic Art in 2004. She is also the associate director of the MahWaff Theatre Company.