The band originally formed in 1989 in Essex, England under the name Blinder. The initial line-up was Daniel Glendining (guitar/vocals), his brother Tom Glendining (drums), Nick Watts (keyboards/backing vocals) and Matt Pegg (bass guitar). The band's main influences were grunge and progressive rock. Following Pegg's departure Blinder rethought their approach, reducing the progressive rock elements in their music. Pegg was replaced as bass player by a friend of the band, Clovis Taylor and, by 1992, Blinder had changed their name to Headswim.
Headswim released two four-track EPs, Tense Nervous Head and Moment of Union, on their own Crush Records label (the eight songs from the two EPs would later be compiled and released as the mini-album Tense Moments). The EPs made enough of an impression for them to be signed by the Sony Music subsidiary Epic Records and they released their debut album Flood in 1994. The album's third single Crawl made the UK Singles Chart. However, the death later that year of Dan and Tom's brother Matthew (who had created all of the band's album artwork up to this point) after a long battle with leukaemia had a profound effect on the group, who took time off to regroup.
Headswim re-emerged in 1997 with their second album Despite Yourself, which contained many cathartic songs about death and spirituality. The group's music had also shifted from their earlier grunge influences to a more reflective alternative rock sound. The lead single Tourniquet reached the top 30 in the UK and was a minor radio hit in the United States. However, Sony made the decision to drop them. The band released only one further single, Dusty Road in 2000 before splitting up in early 2001.

Following the group's split, Daniel Glendining formed a new band, BlackCar, also composing music for film scores. Tom Glendining also played drums for BlackCar while also a member of another band, Tenebrous Liar. In February 2011 it was announced that Dan would be joining his brother Tom in Tenebrous Liar as their new guitarist while continuing to work as BlackCar. Nick Watts became a graphic designer, but is still involved in the music business as he plays keyboards for Mew when they are on tour.

In 2022 Trapped Animal announced the reissue of Flood Redux and the story continues.