Stuart began working with the BBC in the 1970s. She was a continuity announcer and newsreader for both BBC Radio 4 and BBC Radio 2, and in 1980 she played Darong in series one of game show The Adventure Game. She moved to television news in 1981.

Since 27 August 1981, Stuart has presented every news bulletin devised on BBC television apart from the BBC News at Ten. She has also appeared on The News Quiz and presented the news on the BBC's Breakfast with Frost programme each Sunday and the following programme Sunday AM with Andrew Marr. She presented the news for BBC Breakfast during the first half-hour of the programme, three days a week, followed by short half-hourly round-ups throughout the rest of the three-hour-long show. However, BBC Breakfast moved to a new studio with a new look on 2 May 2006 and the entire news content was presented by two main presenters. Stuart retained her slot on BBC's Sunday AM show and continued to present some weekend television bulletins on BBC One. She also worked on other long-form programmes for other BBC channels, including BBC Four.