Plowman attended the Samuel Marsden Collegiate School, New Zealand between 1982 and 1989, where she graduated from Form 7. She later attended the London Academy of Music and Dramatic Art and the Lecoq School in Paris.
Plowman married actor Toby Stephens, who is the son of actors Dame Maggie Smith and the late Sir Robert Stephens, in London, in 2001. In May 2007, Plowman and Stephens had their first child, a son named Eli Alistair. Simon Gray, the renowned British Playwright (who penned Japes, a stage play, and Missing Dates, a radio drama, both of which starred Stephens), was Eli's godfather. Their daughters, Tallulah and Kura, were born in May 2009 and in September 2010, respectively.
Plowman and Stephens performed together as Sibyl and Elyot in Jonathan Kent's revival of Private Lives for the 2012 Chichester Festival, reprised at the Gielgud Theatre in 2013.
