Stevenson started his career with the London-based punk band Chelsea in 1977, while he was still at school studying for A Level exams. He joined Billy Idol in Gen X in 1980 around the time that band's "Dancing with Myself" single was released. After Gen X, Stevenson played for Kim Wilde, contributing to her first album, Kim Wilde, and second album, Select, and performing in all of Wilde's early videos including "Kids in America". Stevenson then formed Hot Club with former Sex Pistols bassist Glen Matlock. They released two singles on RAK Records.
In 1985, he was asked to join post-punk band Gene Loves Jezebel when their guitarist left suddenly at the beginning of their first U.S. tour. Stevenson performed on the band's albums Discover, House of Dolls, Kiss of Life, Heavenly Bodies, VII and The Thornfield Sessions. He produced Gene Loves Jezebel singer Jay Aston's solo album Unpopular Songs, Beki Bondage's solo album Cold Turkey and Gene October's solo album Life And Struggle among others.
During 1994 and 1995, he provided additional guitar playing for the Cult during their world tour. He also contributed guitar to the song "Brand New You're Retro" by Tricky from his Maxinquaye album. He has contributed as a session guitarist on numerous recordings including artists as diverse as Scott Walker, Jimmy Nail, Helen Terry, Annabel Lamb, Louise and the Hothouse Flowers, and has composed music for TV and film.
In 1998, seven years after Mike Peters left the Alarm, he called upon Stevenson to back his solo projects, and the latter has been a permanent fixture in Peters' subsequent musical incarnations, resulting in minor chart success, first under the guise of the Poppyfields with the Top 30 hit "45 RPM" in February 2004, and as the Alarm MMVI with the No. 24 single "Superchannel" in February 2006 (from the album Under Attack).
Stevenson still plays with the Alarm and Gene Loves Jezebel (Jay Aston's version). He also rejoined Chelsea, performing on their Faster, Cheaper and Better Looking (2006) and Saturday Night Sunday Morning (2015) albums. He also plays in Matlock's band the Philistines, and has contributed to Matlock's Open Mind and Born Running albums. He sometimes turns up in New York singer/songwriter Willie Nile's band when they play in the UK.
In 2011, Stevenson and Matlock formed supergroup the International Swingers with vocalist Gary Twinn and drummer Clem Burke. Via PledgeMusic, the band raised the money to record their first full-length album, The International Swingers (mixed by Peter Walsh), which was released in 2015.
In January 2013, Stevenson released a three-track CD, "The Shape of Things to Come", via his own website. An album, Everything's Getting Closer to Being Over, followed in March 2014. The album, produced by Peter Walsh, featured Matlock, Steve Norman, Barriemore Barlow, Geoff Dugmore and others.
Stevenson rejoined the Cult as second guitarist for their "Electric 13" world tour throughout North America, Europe and Australia in summer 2013 and continued to tour with them in 2014.
Since 2014, Stevenson has been playing in the band Holy Holy, performing the music of David Bowie, alongside Mick Woodmansey, Tony Visconti and Glenn Gregory, among others. A recording of their London gig in September 2014 was released by Maniac Squat Records in 2015 as a live album, The Man Who Sold the World Live in London.
His father is the writer John Stevenson. He is married to former Westworld singer Elizabeth Westwood.