Jennifer first found widespread attention in the 1980s when she became a member of The Comic Strip after graduating from the Central School of Speech and Drama. With her comedy partner Dawn French, she wrote and starred in their eponymous sketch show, French & Saunders, for which she and French received a BAFTA fellowship in 2009. She received worldwide acclaim through the early to mid 1990s with her sitcom Absolutely Fabulous writing and playing the lead role of Edina Monsoon.

She has won three BAFTAs (including the Bafta Fellowship), an International Emmy Award, a British Comedy Award, a Rose d'Or Light Entertainment Festival Award, two Writers' Guild of Great Britain Awards, and a People's Choice Award.

She has guest starred in the American sitcoms Roseanne and Friends, and won the American People's Choice Award for voicing the wicked Fairy Godmother in DreamWorks' animated Shrek 2.