He was born in Sheffield, adopted, and moved at an early age with his family to Plymouth. Quantick went to Woodford Junior School in Plymouth, then Exmouth Comprehensive School.
David Quantick began writing for the music publication NME in 1983, alongside Danny Baker and Paul Morley. Together with Steven Wells, he contributed to many of the humorous snippet sections in the paper. In addition to rock journalism, he was also submitting jokes and sketches to British comedy shows such as Spitting Image.
Quantick built his profile steadily and his name began to appear increasingly often in print, radio and television. In 1992, Armando Iannucci asked him to join the writing team for the Radio 4 spoof news programme On the Hour, after which he made the natural progression to the television follow-up The Day Today (BBC2, 1994). Both shows were highly acclaimed and won awards, and secured a loyal cult following.
Quantick ceased submitting copy to the NME in 1995, and around this time, he was appearing regularly on Collins and Maconie's Hit Parade (Radio 1, 1994–1997), commenting astringently upon music's stars. This developed into his own named slot in the show, named Quantick's World. His connection with Maconie continued in parallel on the weekly show, The Treatment on BBC Radio Five Live, which was an hour-long satirical news round-up.
In 1995, Carlton Television broadcast a set of six pilot television shows, one of which was Now What? The series was not picked up for development but Quantick found a writing partner through these proceedings in Jane Bussmann. The two went on to write and perform Bussmann & Quantick Kingsize (1998), a series of sketches and monologues for BBC Radio 4.
Quantick rejoined Chris Morris to write for Brass Eye in 1996 (broadcast in 1997). He also wrote for Morris's radio series Blue Jam (Radio 1, 1997) and the subsequent television version Jam (Channel 4, 2000). The 2001 Brass Eye Special attracted so much protest that Government ministers promptly condemned the programme without having seen it.
Throughout this period, he also contributed to less provocative fare such as Smack the Pony (Channel 4, 1999–2001), Harry Enfield's Brand Spanking New Show (Sky One, 2000) and could be heard on Radio 4's The 99p Challenge.
In 2000, Quantick and Bussmann created the world's first internet sitcom Junkies about three heroin addicts. Quantick also claimed it as the first docusitcom (documentary/sitcom). It starred long-time Morris collaborator Peter Baynham, with Sally Phillips (Smack the Pony) and Peter Serafinowicz (Look Around You). The project grew out of the writing pair's frustration with the commissioning process. The average sitcom, they said, costs £200,000 to make and finding funds is too difficult. So they secured the services of cast and crew on a voluntary basis and made a show for less than £4,000. The site received over a million visits in its first eight months of existence.
In 2001, Quantick collaborated with Collins and Maconie again on Lloyd Cole Knew My Father, a live show where the three recounted humorous tales of working as rock journalists. Stories were mainly concerned with the deflating aspects of the job, such as the boredom, missing assignments, and the idiosyncrasies of fan letters. A performance was later broadcast on Radio 2 as a six-episode series.
Around this time, Quantick took part in a number of nostalgic list shows on British television themed around decades past: I Love the 1980s and I Love the 1990s etc.
In 2003 and 2005, Quantick contributed material to sketch show That Mitchell and Webb Sound, and co-wrote five series of 15 Minute Musical (2004–08) with Richie Webb, whom he also wrote with on several series of Parsons and Naylor's Pull-Out Sections. He also made several appearances on Clive Anderson's radio panel show We've Been Here Before in 2003 and 2004. 2005 also saw him take part in Channel 4's Come Dine with Me, with four other celebrities. Throughout, Quantick worked on biographies of musicians and comedians (The Clash, Beck, Lenny Bruce, Richard Pryor and Bill Hicks).
Quantick continues to write, and co-presents a weekly programme One Way Single Parent Family Favourites on art radio station Resonance FM. He was also part of the writing team of Harry Hill's TV Burp, and writes and presents series 3 of 'The Blagger's Guide', a six-part comedy series on BBC Radio 2 with writer and producer Simon Poole. He also appears as Doctor Dave Radio on another Radio 2 comedy programme, Radio Rivron.
In 2006, Quantick recorded One — his first solo BBC Radio 4 series. A show in which no sketch featured more than one voice, it received excellent reviews and featured a variety of performers and writers, including Graeme Garden, Bill Oddie, Dan Maier, Kevin Cecil and Jeremy Clarkson. He also made two appearances on the radio show Clive Anderson's Chat Room in 2006 and 2007.
On 3 April 2008, music magazine The Word was forced to apologise in court to Morrissey, over an article by Quantick that accused the singer of racism and hypocrisy. In June 2008, Quantick was recruited as one of the launch presenters of Q Radio, presenting a weekly show. He will also write a column for Q magazine.
Quantick regularly stood in when Stephen Merchant was unavailable for his Sunday afternoon BBC 6 Music radio show, and occasionally stands in for other broadcasters on the station. In 2007, he wrote the Doctor Who audio play 'The Dark Husband' featuring the 7th Doctor, Sylvester McCoy, for Big Finish Productions.
In 2009, Quantick made two more appearances on the radio show Clive Anderson's Chat Room.
In 2012, having worked on the final series of TV Burp, Quantick contributed material to The Thick of It, continued to write for Rob Brydon, and recorded further editions of The Blagger's Guide for Radio 2. In September of that year, he published an e-book novel, Sparks, described by Neil Gaiman as "excellent"
In 2014, Quantick made a four-episode comedy series 52 First Impressions with David Quantick for Radio 4 in which he recounted stories about 52 individuals he had encountered in his life/career.
In 2015, Quantick received an Emmy for his work on the HBO Series, Veep
In 2015 Quantick successfully crowd-funded a novel "The Mule" via the Unbound (publisher) company which was released on 25 February 2016.