She has made numerous television appearances, including as Mrs. Brazendale in the BBC TV series Lilies.
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.
As a child, Hennessy was a member of the St Winifred's School Choir which reached number one on the UK Singles Chart in 1980 with the song "There's No One Quite Like Grandma".
[2] She also starred in BBC One drama Dickensian, a series based on Charles Dickens' characters.
She returned to Doctor Who in 2017, playing Moira, the foster mother of Bill Potts.