Her parents parted ways while Grainger was very young. Her mother raised her. Despite not having a lot of money growing up, Her mother made sure that Grainger will take lessons in ballet, piano, martial arts and gymnastics.
When she first appeared on television, she was only 6 years old. She played a part on the dramatic comedy series titled All Quiet on the Preston Front. Though Grainger once admitted in an interview that she started acting as a passion and as a hobby but gradually she started loving her profession as she grew older. She became so dedicated that she even left her studies at Leeds University because she was offered a role on the BBC series Waterloo Road. She took the role and was well appreciated for that as well.
Grainger's took giant leaps forward after she was made her film debut in 2009. She made her silver screen debut as a young runaway in The Scouting Book for Boys. After which, she has had played significant parts in films such as Anna Karenina, Bel Ami, and Great Expectations.
She garnered huge limelight after starring on the famous American TV series The Borgias and by playing Bonnie Parker in Bonnie and Clyde in 2013.