Williams first joined The Cure in 1984 (first gig on 7 November in Minneapolis, Minnesota, USA), replacing Andy Anderson, who was fired for destroying a hotel room after a racially motivated incident with a security guard . During his tenure, Williams helped The Cure reach their critical and commercial peak recording the studio albums The Head on the Door, Kiss Me, Kiss Me, Kiss Me, Disintegration, and Wish.

Williams left the band in 1994. His last concert was on 13 June 1993 in Finsbury Park at a benefit concert for London’s XFM radio station. He started another band called Babacar with his then-girlfriend Caroline Crawley. He briefly reunited with The Cure for the acoustic recording of their Greatest Hits compilation in 2001, but he did not rejoin them officially. He was also present at some of the sessions for the Cure’s 2004 album, simply titled The Cure.