Cohu's first acting job after graduating from drama school was at the Royal Exchange Theatre in Manchester, in a production of Jane Austen's Pride and Prejudice. She made her television debut in an episode of Casualty. She went on to work extensively in television, including playing the role Major Jessica Bailey in the popular ITV show Soldier Soldier followed by many parts in British television. In 2005 she portrayed Princess Margaret in the semi-fictional version of her life, The Queen's Sister, for Channel 4, for which she was nominated for Emmy and BAFTA awards. She was widely praised for the role; for Example, Variety disliked the "somewhat tawdry biopic", but said that "Cohu makes it all worth watching". Cohu herself said she played Margaret like a proper woman with an insatiable and tremendous Energy for life: previous images in her mind had been of a bloated and sick courtier confined to a wheelchair. She hoped the production hadn't offended anyone as she really liked the Queen.