Macqueen was a member of the National Youth Theatre between 1992 and 1995, then trained as a barrister at the Middle Temple. He worked as a Business Affairs Executive for Granada International and has worked in the House of Commons with a member of the Culture & Media Select Committee, specifically working during the creation of the Broadcasting Act 1996.
Macqueen was educated at St John's School, Leatherhead and left to receive a first in English literature at Durham University. He went on to study for a M.Phil at Pembroke College, Cambridge, graduating in 1998.
He is perhaps best known for his recurring role as sarcastic consultant anaesthetist Keith Greene, appearing in 75 episodes of Holby City between May 2005 and July 2010. He appeared as Julius Nicholson, the "blue-skies advisor" to the Prime Minister in political satire The Thick of It and as Sir Jonathan Tutt, British Ambassador to the UN, in the film In the Loop, both directed by Armando Iannucci.
Macqueen has appeared in a series of videos on YouTube as Clive Rudloe, a character who claims to be "the world's number one DJ". The videos are spoofs created by real-life DJs Above and Beyond. In late 2009, he starred in several episodes of The News at Bedtime on BBC Radio 4, in a variety of supporting roles.
In 2010, he appeared as the publisher Malcolm Dodds in Woody Allen's You Will Meet a Tall Dark Stranger. That year he also had a small role in the comedy film Four Lions. In 2011, he appeared in "The National Anthem", an episode of the anthology series Black Mirror.
In 2012, he appeared in a Doctor Who spin-off UNIT: Dominion, published by Big Finish Productions, in a role described as "the Other Doctor" who is revealed to be the Master. He reprised this role in 2014 for Dark Eyes 2, Dark Eyes 3 and Dark Eyes 4. He reprised the role again in 2016 alongside Geoffrey Beevers, who had played an earlier incarnation of the Master, in The Two Masters. He also appeared in a lead role as Edmund in Julia Davis' black period comedy Hunderby, opposite Davis and Alexandra Roach.
In 2015, he also played the royal crier in Cinderella. In 2016, he appeared opposite Sir Michael Caine in the film Youth, and played the role of Patrick Jarvis MP in series 3 of Peaky Blinders.
