Amara was born to Sri Lankan parents who had moved to England from Zambia to further her father's work opportunities. She went to the Wimbledon High School and, although she enjoyed drama, she regarded acting as a risky profession and studied Politics, Philosophy and Economics at Oxford University, graduating with a 2:1 degree. She then spent two years working in the City of London dealing in mergers and acquisitions. Whilst at Oxford she had directed and appeared in plays and finally decided to go to drama school. Within a month of graduation she was auditioning for Wes Anderson's film 'The Darjeeling Limited'.