The single was released on 10 March 2008 as the band's first release on Fiction Records across two 7" vinyl records and one CD single. The song marked the band's joint-highest charting single at the time, peaking at No. 19 on the UK Singles Chart, becoming also their third UK Top 20 success and their sixth UK Top 40 entry. It was to be bettered four years later by their succeeding single "One Day Like This" - which was performed by the band in the closing ceremony of the 2012 Summer Olympics, peaking at No. 4 in August 2012. Frontman Guy Garvey told Uncut that "'Grounds for Divorce' was written when I was in an unhappy relationship." On 21 May 2009, "Grounds for Divorce" won the Ivor Novello award for Best Contemporary Song.
"Grounds for Divorce" was featured in the promotional trailer for Valve Corporation's 2008 game Left 4 Dead, and in the trailer for the 2008 film Burn After Reading. An instrumental version was also featured on Series 12, Episode 1 of the British motoring show Top Gear and was played at the opening montage which contained clips from the upcoming episodes, as well as in the third episode of the same series.
"Grounds for Divorce" was also featured in the eighth episode for the 5th season, and promos for the sixth season of the TV-show House MD. Also appeared in episode 521 of Rescue Me. It appeared in the soundtrack of DiRT 2, a rallying video game and was also used as the end credits song for an episode of Pete versus Life. In 2009, the riff was used on the The Hairy Bikers' Food Tour of Britain TV show, whilst showcasing the professional chef opponent in the taste-off, as well as by The Apprentice contestant Chris Bates, in the final episode of series six in an advert for an alcoholic drink. The song is also on the soundtrack for a 2011 video game, Driver: San Francisco and also on the soundtrack for a 2015 video game, Guitar Hero Live.