After working in specialist journalism on the oil industry, she joined the BBC in 1983. At first she reported on financial news and worked as a radio producer, later moving into television as presenter of Newsnight and (briefly, after serious illness) on The Money Programme on BBC2. In the mid-1990s she presented BBC2's The Antiques Show with Tim Wonnacott and was one of the original presenters of BBC Radio 4'sFront Row in 1998. She later moved to The Film Programme on radio, which she still presents. She is also the regular host of the BAFTA Life in Pictures strand, and regularly writes about film for Prospect magazine.
Since 2005, she has been chair of the Tate Members Council and became the first female Honorary Fellow of Jesus College in 2007. As a novelist, Stock has published two works of fiction: A Foreign Country (1999, shortlisted for the Whitbread First Novel award) and Man-Made Fibre (2002).
She is married to Robert Lance Hughes; the couple have two daughters.