Stubbs made an impressive debut as the reactive title character in the British-French co-production "Nanou" (1987), which briefly featured Daniel Day-Lewis as the heroine's friend. Subsequently she offered a poignant performance in Piers Haggard's "A Summer Story" (1988), a period drama which saw her cast as a young woman whose heart is broken by a caddish barrister (James Wilby) and won praise as a seductive Norse princess in Terry Jones' "Erik the Viking" (1989). She seemed slightly miscast as a Senator's daughter in her American feature debut, "True Colors" (1991) but bounced back in two 1995 films. She was briefly seen as Richard E Grant's wife who dies in childbirth in "Jack and Sarah" and was Emma Thompson's rival for Hugh Grant's affection in Ang Lee's "Sense and Sensibility". Stubbs co-starred as Viola in "Twelfth Night" (1996), directed by her husband Trevor Nunn.
Television has perhaps provided Stubbs with her widest audience. After co-starring in the British miniseries "The Rainbow" (shown in the US in 1989 on A&E), she tackled the lead in a series of TV-movies centering on a former policewoman now working as a private detective. As "Anna Lee", Stubbs garnered critical praise and positive comparisons with Helen Mirren's "Prime Suspect" character, Jane Tennison. To date, six installments have been aired in the US on A&E.