Rew is from Bristol and his family moved house several times during his boyhood. He joined Harrow County School for Boys at the age of 14, being known for being good at Ancient Greek and Latin, and playing the guitar.[2] He lived at 206 Torbay Road, in South Harrow. In 1970, he gained a place at Jesus College, Cambridge, to study Modern Languages, on an exhibition. Another boy from his school joining the university at the same time was Geoff Egan. At Cambridge, Rew gained a degree in archaeology, receiving a 2.1,[3] and settled in that city.[4]
The group was named after the novel The Waves. The drummer Alex studied History at Cambridge. The group first played together at the Galaxy Club at RAF Mildenhall in 1980.[5]
In 1981, the Soft Boys' leader Robyn Hitchcock began his solo career; Rew and Cooper joined with Katrina Leskanich and Vince de la Cruz to form Katrina and the Waves. The group survived a slow career climb by tours of RAF bases and Canadian club gigs, then teamed up with the producers Pat Collier and Scott Litt to record Rew's compositions "Going Down to Liverpool", covered by The Bangles, and, in 1985, "Walking on Sunshine", which became the group's first and biggest hit.[6]
In 1997, Katrina and the Waves won the Eurovision Song Contest for the United Kingdom with the Rew composition "Love Shine a Light". The song was written for the Samaritans 30th anniversary.
In 1999, Leskanich left the band to pursue a solo career. Rew continued to write, record and release solo albums. From 1988 through to 2004, he was a guest member of the Cambridge band The Lonely. He played on three albums, Underground (1989), Rarer Gifts (1998) and Live (2000).
In 2001 Rew reunited and toured with Robyn Hitchcock, bassist Matthew Seligman, and Morris Windsor for the Soft Boys' re-release of their 1980 album Underwater Moonlight. The following year they recorded and released a new album, Nextdoorland, which was accompanied by a short album of outtakes, Side Three.
In 1997 Rew was living on Mill Road, Cambridge.[4] In 2004, he joined the Cambridge band Jack, which his wife Lee Cave-Berry had already joined in 2000. The two also perform together as a duo called Kim and Lee.[7][8]