Annett has spent time in America, where she had a part in the 1992 TV miniseries Jewels. Back in Britain, most of her roles were "bit parts", although she played the starring role of Holly Turner in Crime Traveller in 1997 alongside Michael French, who played Jeff Slade. In 1992, she played the part of Gertrude Winkworth in one episode of the Granada's series Jeeves and Wooster, based on the novels of P.G. Wodehouse, in which Hugh Laurie and Stephen Fry starred. She also played Angela Mortimer, the great-niece of Mrs Pumphrey and the love interest of Tristan Farnon, in one episode ("Hampered") of All Creatures Great and Small.
Annett remains best known for taking over the role of Kristine Kochanski in the seventh and eighth series of the British science fiction comedy television series Red Dwarf, a role which she reprised in the final part of the 2009 special, Red Dwarf: Back to Earth.
She won Best Actress at the April 2011 London Independent Film Festival.