Nelson was educated at the Wakefield College of Art, where he developed an interest in the work of poet and filmmaker Jean Cocteau. At this time he was also developing as a musician, drawing upon Duane Eddy as a primary guitar influence. A locally produced solo album titled Northern Dream drew the attention of famed British DJ John Peel, and this eventually led to Nelson's new band, Be Bop Deluxe, signing to EMI Records. The band developed a reputation built upon Nelson's electric guitar stylings, which have been described as "pyrotechnic".
After the breakup of Be Bep Deluxe, Nelson attempted another band project called Red Noise, but eventually settled into a career as a solo musician, recording iconoclastic albums in the early electropop vein such as The Love That Whirls and Quit Dreaming and Get On the Beam. Many of these albums also shipped with bonus records featuring experimental ambient instrumentals, and this was a genre of music Nelson would embrace more fully in the future.
Nelson had bad luck with major labels in the 1980s. A deal with CBS Records went sour, leaving one admired album, Getting the Holy Ghost Across (US title: On a Blue Wing) in limbo with no CD release to this day. Nelson and his manager Mark Rye had formed the Cocteau Records label in 1981, and for many years this label handled the majority of Nelson's output, which often included multiple albums a year. Among the more ambitious Cocteau releases were the four-record boxed set of experimental electronic music, Trial by Intimacy (The Book of Splendors), and the later ambient collection, Chance Encounters in the Garden of Lights, which contained music informed by Nelson's Gnostic beliefs. In the late 1980s, Nelson signed to the US label Enigma Records, and though they re-released his entire Cocteau catalog and seemed to be giving him a big push, the label soon went out of business.
As the 1980s ended, Nelson suffered a tremendous series of personal setbacks, including a divorce, tax problems, and an acrimonious falling-out with his manager over his back catalog rights. In the case of one album, the unreleased Simplex, his manager had been selling copies via mail order without Nelson's authorization.
Nelson channeled his troubles into his music, with the result that the 1990s proved an even more prolific period for him. His divorce inspired a 4-CD boxed set, Demonstrations of Affection, and he worked on some guitar-based instrumental projects such as the albums Crimsworth and Practically Wired, or How I Became Guitar Boy. With Demonstrations, Nelson perfected a songwriting ethic based on the immediacy of creative inspiration; each song was recorded almost as soon as it was written, taking only an average of two hours to complete. This technique enabled Nelson to produce a staggering amount of new music into the new century, which resulted in such large-scale releases as the 4-CD set My Secret Studio and the 6-CD set Noise Candy.
Nelson today has a label, Populuxe Records, that has a distribution arrangement with Robert Fripp's Discipline Global Mobile. Though not a very public figure today, Nelson has a devoted core audience who admire his perseverance, his integrity to his art in the face of commercial rejection, and his versatile musicianship. In recent years Nelson has begun to perform live again.