The Clash quickly became one of the leaders of the burgeoning punk rock movement in the U.K. (along with such outfits as the Sex Pistols, the Damned, Siouxse & the Banshees, etc.), signing on with Epic Records soon after. With Jones and Strummer co-writing almost all of the tracks, the Clash issued such rough and ready punk classics as 1977's self-titled debut and 1978's Give 'Em Enough Rope. But it was 1979's double album London Calling that the group truly came into their own. Often considered to be one of rock's all-time best releases, the musically varied album scored one of their biggest hit singles, the Jones-sung "Train in Vain." Further releases followed, such as 1980's triple album set Sandinista! and Combat Rock (the latter of which featured another Jones-sung hit single, "Should I Stay or Should I Go"), which saw the group expand their sound even further; resulting in the Clash becoming one of the top rock bands in the world. It was also during the early '80s that Jones produced a few other artists (singer Ellen Foley and former Mott the Hoople leader Ian Hunter), and guested on a B-side by Elvis Costello.

But widespread success created tension between Jones and the other bandmembers, leading to his exit from the band in 1983 (Simonon and Strummer would keep the Clash afloat for one more release, 1985's best-forgotten Cut the Crap). Jones' next project, Big Audio Dynamite, was launched in 1985, and provided the freedom to experiment with other styles (mostly funk/dance-based), as he was joined by video artist Don Letts (who also provided vocals and effects), drummer Greg Roberts, keyboardist Dan Donovan, and bassist Leo "E-Zee Kill" Williams. A steady stream of albums followed from the mid- to late '80s, including 1985's This Is Big Audio Dynamite, 1986's No. 10, Upping St. (produced by ex-Clash mate Strummer), 1988's Tighten Up, Vol. '88, and 1989's Megatop Phoenix. Most of BAD left around this time (forming the group Screaming Target), while Jones soldiered on with new members Nick Hawkins (guitar), Gary Stonadge (bass), and Chris Kavanagh (drums), changed their name to Big Audio Dynamite II, and issued such further releases as 1991's The Globe, 1994's Higher Power, and 1995's F-Punk. During the late '90s, rumors of a Clash reunion began to surface regularly, but despite the fact that all former members were back on good terms, the invites were turned down; but Jones and his former Clash bandmates were interviewed extensively for the bio-movie Westway to the World, and Jones began DJing with some of his BAD bandmates at the Maximum club in London.