At the beginning of their writing career, Armstrong and Bain wrote for the Channel 4 Sketch show Smack the Pony and the children's shows The Queen's Nose and My Parents Are Aliens. They went on to create and write Peep Show, BBC One sitcom The Old Guys, and most recently Channel 4 comedy-dramas Fresh Meat and Babylon. They also wrote for the Radio Four Sketch show That Mitchell and Webb Sound, starring Peep Show's two main actors David Mitchell and Robert Webb, and its BBC Two adaptation That Mitchell and Webb Look. Peep Show has won several writing awards, including a BAFTA for Best Situation Comedy in 2008.

Alongside Armando Iannucci, Simon Blackwell and Tony Roche, Armstrong wrote for the first three series of the BAFTA-winning BBC Four comedy The Thick of It, and its 2009 film spin-off In the Loop. In The Loop was nominated for the Academy Award for Best Adapted Screenplay in 2009, and won Best British Screenplay at the 2009 Evening Standard British Film Awards. Alongside The Thick of It's writing team, Armstrong wrote one episode of the first season of HBO comedy series Veep, set in the office of the American vice-president.

In 2010, Armstrong's currently-unproduced screenplay Murdoch, a drama in which Rupert Murdoch and his family disagree over who should have control of his company, received attention after it appeared on The Black List, a list of unproduced screenplays most liked by Hollywood industry figures. In the wake of the 2011 phone hacking scandal involving newspapers owned by Murdoch it was rumoured that the script was being developed by Channel 4, but Armstrong dismissed these claims.

In October 2011 it was reported that Armstrong's film adaptation of Richard DiLello's book The Longest Cocktail Party, charting the founding of The Beatles' record company Apple Records and the recording of their final album Let It Be, was to be directed by Michael Winterbottom. In February 2016 it was reported that Winterbottom had withdrawn from the project and the film's Future was uncertain.

In 2012, Armstrong and Bain wrote the Channel 4 comedy pilot Bad Sugar, a spoof of Dynasty-style soap operas, which stars Olivia Colman, Julia Davis and Sharon Horgan, all of whom also co-conceived the show.

To date, Armstrong and Bain have written two films together – the 2007 comedy Magicians, and, alongside Chris Morris, the 2010 terrorism satire Four Lions.

In 2014 Armstrong, with Danny Boyle, Robert Jones and Sam Bain, co-created the Channel 4 comedy-drama Babylon. Armstrong wrote the first and last of the 6 initial episodes and co-wrote the pilot with Sam Bain.

Armstrong's first novel, Love, Sex and Other Foreign Policy Goals, was released in April 2015.

In 2017, Armstrong's American drama series Succession executive produced by Adam McKay and Will Ferrell was picked up to series by HBO.