Frostrup was born in Oslo but moved with her family as a child to Ireland, living in Kilmacanogue, a small village south of Dublin in County Wicklow. Her Norwegian father, who died aged 44, was a journalist on the Irish Times, and her Scottish-born mother an artist. In 1977, she left Ireland and moved to London. There, she worked as a public relations executive for Phonogram Records, between 1980 and 1990; marshalled the PR for the Live Aid concert at Wembley in 1985; and, after leaving Phonogram, swiftly broke into television as a film critic, presenting Thames Television's Video View from 1990 and—after Thames lost the London ITV franchise, reprised the role straight afterwards on The Little Picture Show for Carlton Television from 1993.[citation needed]

Frostrup has interviewed many different celebrities, writers and other artists and has presented a variety of different TV programmes, including one on travel, and has appeared in other TV shows such as the series Have I Got News for You and the sitcom Absolutely Fabulous. She made several guest appearances as herself in the series Coupling including an episode where one of the characters fantasizes about her, then meets her in person.[citation needed]

Frostrup presented the BBC Radio 2 show, The Green Room, and also regularly presents Open Book (most Sundays and Thursdays) on Radio 4. Her political views have been described as "a bit left-of-centre".

She writes for The Guardian, The Observer, The Mail on Sunday, Harpers & Queen and the New Statesman. She is also an art critic and has been on the judging panels for the Man Booker Prize, the Orange Prize for Fiction and the Evening Standard British Film Awards.[citation needed]

In September 2007 she chaired a question-and-answer session with British Prime Minister Gordon Brown, at the Labour Party Conference in Bournemouth, Dorset.

Currently she presents the weekly book show on Sky Arts 1 called The Book Show where she interviews her extensive list of guests on their recent works and their "favourite heroes and heroines from fiction".[citation needed]

In September 2009, the nature film The Crimson Wing: Mystery of the Flamingos was released in the United Kingdom, for which Frostrup provided the voice-over.[citation needed]

She is close friends with actress Gina Bellman, one of the stars of the aforementioned Coupling, in which she had a cameo role alongside Angus Deayton.