After her graduation in 2001, Poulet landed her first role in the television series The Bill. In 2005, she portrayed Camilla Parker Bowles, now the Duchess of Cornwall in the television film Whatever Love Means. She appeared in the feature film In the Loop in 2009. The same year she portrayed Carol Thatcher in the television film Margaret. She has also had roles in Day of the Flowers, Sherlock, Dappers, The Thick of It, Reggie Perrin and Outnumbered.