Peterman was born and raised in Edgbaston, Birmingham. From years two to 18, Peterman attended Edgbaston High School for Girls. At 14, Peterman was scouted by London's Models 1 modeling agency, working with them until matriculating to drama school. She is of Welsh and Polish Ashkenazi Jewish descent.
Peterman's maternal great-grandmother was the Yiddish theatre actress, Becky Goldstein. "Born in Mlava, Poland, moved to England at the age of 12. She became an actress at the Pavilion later transferring to the Grand Palais. A specialist in archetypal 'Yiddishe mama' roles, she left the stage owing to ill health." Goldstein was married to the actor and playwright, Joseph Markovitch, who "joined the Pavilion Theatre as an actor and playwright. A prolific dramatist and lyricist, he wrote such plays as The Revolutionary, Mendel Beilis, The Gambler, The Two Chaverim, and The Desert. In later years, until his retirement in 1960, he belonged to the Grand Palais company."
After a three-year degree course at Arts Educational Schools, London, Peterman starred in various stage roles. Peterman then undertook a series of supporting roles in various television productions, including: Footballers Wives, Dream Team, Hotel Babylon and Lip Service. She first starred in Doctors, as Phoebe Billington, in a single episode in 2009, but returned in 2011 to play murdered receptionist, Lauren Porter. Her performance garnered a Best Storyline and Best Episode nomination at the 2011 British Soap Awards.
In 2013, Peterman played the role of Natalie Fisher in the HBO/Sky1 British action and military television series, Strike Back.
Peterman can be seen in Survivor, the 2015 British-American spy thriller film starring Pierce Brosnan, Milla Jovovich, and Dylan McDermott, and directed by James McTeigue.
Peterman starred as the lead in the Syfy channel made-for-television movie, Roboshark, which kicked off Sharknado week 2015.
Peterman co-owns the London café and venue space, Drink Me Eat Me, with her partner, actor, Dar Dash.