Martin was born in Solihull - West Midlands in England. Her father is Scottish and her mother is English. She is the third of four children. She attended a local secondary school in Knowle until the age of sixteen, when she was awarded a scholarship on the Musical Theatre course at Tring Park School for the Performing Arts. At seventeen she got a part in Dirty Dancing on London's West End. She then went on tour around the world in Mamma Mia and returned to the West End at twenty-one to play the role of Lorraine in Jersey Boys.
She also studied at BTEC, working on a diploma in performing arts, concentrated on acting for screen. Martin's first TV role was Penny in the series Riviera.