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.
Poulet has also appeared on stage productions including The Queef of Terence and The Bird Flu Diaries. She has also voiced roles in video game Dragon Age II by BioWare. In 2011, Poulet and her comedy partner Sarah Solemani wrote a sitcom for the BBC, which will be produced by Charlie Hanson. She also completed a screenplay called Ocean Road for Producer Harriet Rees.
In 2018 she joined the cast of Holby City playing the hospitals new Consultant cardiothoracic surgeon Abigail Tait.
Poulet is an ambassador of The Park Theatre. She appeared in Sarah Rutherford’s Adult Supervision, at the Park Theatre in Finsbury Park.