Munden began his career as an assistant to Mike Leigh, Derek Jarman, and Terence Davies before directing documentaries for television at the BBC.
His first film, Bermondsey Boy (1991), was a documentary examining some of the myths of masculinity, which won a Silver Plaque at the Chicago International Film Festival and was nominated for the BFI Award for Innovation.
In 2007 Munden directed The Mark of Cain, picking up the BAFTA Award for Best Single Drama and earning Munden his first nomination for Best Director. He also received BAFTA nominations for The Devil’s Whore (2009) and The Crimson Petal and the White (2011).
Munden went on to direct the cult hit Utopia (2013–2014). The series received high praise for its striking visuals, but also some expressions of concern about its violence. Mark Monahan of The Daily Telegraph described it as “a dark, tantalisingly mysterious overture,” while Sam Wollaston of The Guardian called it “a work of brilliant imagination,” “a 21st-century nightmare” that “looks beautiful,” but also wondered about the gratuitousness of its violence. The series won an International Emmy Award for Best Drama Series in 2014 and Munden received a BAFTA nomination for Best Director.
In 2016 Munden directed National Treasure starring Robbie Coltrane and Julie Walters, winning the BAFTA for Best Director and Best Miniseries.
In 2018 it was announced that Munden was to helm the film The Secret Garden for David Heyman & Studiocanal. Based on Frances Hodgson Burnett’s 1911 book, the story centers on Mary Lennox, a troubled, sickly, 10-year-old orphan who is sent to live with an uncle in England when her parents die in a cholera outbreak.
In 2020, Munden reunited with Utopia creator Dennis Kelly, directing the first three episodes of Kelly's HBO miniseries The Third Day.