Across the pond, Jensen has achieved success as a cast member of the ABC series Ugly Betty and the short-lived CBS sitcom Accidentally On Purpose.
After coming to attention with her first major television role as Clare Donnelly in 1993 BBC drama Down Among The Big Boys, in which she played the daughter of Billy Connolly's character, Jensen's first comedic appearance came in the final series of BBC comedy May To December. Shortly thereafter, she was offered the part of the socially inept Maggie Jacobs in the BBC Two/HBO comedy series Extras, co-starring with Ricky Gervais. For her work on this show she would receive best television comedy actress and newcomer awards at the 2005 British Comedy Awards. The year after, she won two more British Comedy Awards and a BAFTA nomination, and her role in the 2007 Christmas special earned her an Emmy Award nomination.
Following the success of Extras, Jensen took on her first significant role in US television, playing regular character Christina McKinney on the ABC series Ugly Betty. Although this role was originally intended for an American actor, when she met the show's producers they liked her accent and personality and changed the nationality of the character. She left the show in 2009 after the city of production was changed to West-Coast America.
In January 2009, Jensen starred in No Holds Bard, a BBC Scotland one-off comedy special celebrating Robert Burns, and in this same year she premiered in the American CBS sitcom Accidentally On Purpose, playing Olivia.
In 2014 Jensen a central protagonist role in the Sky One crime-based comedy drama Agatha Raisin, in which she plays an amateur detective. Starring alongside Katy Wix and Mathew Horne, her PR whizz character gives up a successful life in London and take-up residence in the village of Carsely, hoping to begin a new dream life. In 2015, Jensen began her role as Fran in the Channel 4 sitcom Catstrophe, playing the friends of the central couple, played by Sharon Horgan and Rob Delaney.
In March 2019, Jensen reunited with Ricky Gervais on the Netflix dark comedy series After Life, about a cynical, pessimistic man who can hardly see the point of life after his wife dies from breast cancer.
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