Hennessy trained for three years at the Central School of Speech and Drama, graduating in 1992. She has since appeared in a number of theatrical roles, as well as on television, including the character of Jude in The Office; Julie, the man-hating shop-assistant, in the "Fockin Mokky Bokka" episode of Two Pints of Lager and a Packet of Crisps; and, in 2007, as Valerie Brannigan (the wife of Ardal O'Hanlon's character, Thomas Kincade Brannigan) in "Gridlock", an episode of Doctor Who, playing a vet in the BBC3 comedy "Pulling" (2008) and in the BBC mini-series South Riding in 2011.