Duff was born and raised in Hayes End, West London by Irish parents. She attended Mellow Lane School, Hayes End, Hillingdon. She studied acting at The Drama Centre, now part of the University of the Arts London, having initially also applied to art colleges.

Her father convinced her that she was not an artist and told her to persevere with acting. She took another year out after A-Levels before being accepted to The Drama Centre.

She is married to fellow actor (and former Shameless co-star) James McAvoy.

In 2000, Duff was nominated for a Laurence Olivier Award, but first became well known as Fiona in the television programme Shameless, and for her portrayal of Elizabeth I of England in the lavish 2005 BBC television miniseries, The Virgin Queen which also starred Joanne Whalley and Tara Fitzgerald.

An accomplished theatre actor, she has worked extensively with the Royal National Theatre and also in London's West End (Vassa, Collected Stories). Theatre credits for the National Theatre include Collected Stories, King Lear Notes on a Scandal.