Macqueen was born in Epsom, Surrey. He was educated at St John’s School, Leatherhead, and left to receive a first in English literature at Collingwood College, 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. He also appeared in the Comic Relief special of Mr. Bean in 2007 as the vicar.

Macqueen has appeared in television advertisements for Specsavers, Dell, and Utterly Butterly. He appeared in the Comedy Central/BBC collaboration, Kröd Mändoon and the Flaming Sword of Fire, in which he played Barnabus, the sidekick to the Chancellor Dongalor, played by Matt Lucas. He starred as Roy Tunt in The Hide, which premiered on FilmFour in February 2009. He won the award for Best Actor at the Marbella Film Festival in 2009 for this role.

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.

He played the role of Hove in the 2015 BBC series Pompidou, starring alongside Matt Lucas. He played Luke, the senior doctor in the six-part ITV comedy The Delivery Man.

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.