Martha trained at RADA, having previously been a member of the National Youth Theatre.
Her theatre credits include Don Juan Comes Back from the War at the Belgrade Theatre, Suzy in Inside Job and Jacqueline in Don't Dress For Dinner at the Sheringham Little Theatre, Hermione in The Winter's Tale Retold for Theatre Alive, Lucy in Up on the Roof at the Arcola Theatre, and The Girl in Sarah Kane's Psychosis 4.48 at Studio Three.
Martha's screen experience has included playing Lilly in the feature film Private Moments, and the short film Pitch Perfect, which was nominated for the Best Short Film prize at the British Independent Film Awards. She also plays Jeanette in the soap opera Arabs in London.
Martha has performed with the British Shakespeare Company, with whom she played Helena in A Midsummer Night's Dream, Rosalind in As You Like It , Princess Katherine in Henry V, Beatrice in Much Ado About Nothing and Kate in The Taming of the Shrew for the Leeds Festival.