Anna Charlotte Martin was born in Beverley on 10 May 1977 to Rosalind (née Youngson) and Ivan Martin. Her father was managing director of a pharmaceutical company and her mother was a research scientist. Her mother gave up her job to bring up Anna and her elder brother, Adam.
She attended Beverley High School, where she appeared in school plays. After she left school, Martin studied history at Liverpool University.
After completing her education at Liverpool, Martin enrolled to study acting at London Academy of Music and Dramatic Art (LAMDA). She added the name Maxwell (her maternal grandfather's first name) to her name to distinguish her from another member with the same name when she joined Equity. In 2022, Martin appeared on an episode of Who Do You Think You Are?, and said that Maxwell is a middle name and not part of her surname.
