Born in Manchester, Hannett was raised in a working class, Catholic family in Miles Platting, Manchester; he attended Corpus Christi school and Xaverian College in Rusholme. In 1967, he went to the University of Manchester Institute of Science and Technology (UMIST), where he earned a degree in chemistry but chose not to pursue the profession.
Hannett's uncle was a bass player and gave his nephew a bass guitar when he was 14. Hannett played bass with Spider Mike King and as member in a band called Paradox, in 1973, alongside Paul Young, later of Sad Café and Mike + The Mechanics.
His production work began with the animation film soundtrack All Kinds of Heroes, written by Steve Hopkins (with whom Hannett later worked again). By this time, he also began to mix live sound at pub gigs. Other early production works included Greasy Bear material, Belt & Braces Road Show Band's eponymous album in 1975 and five songs from Pete Farrow's repertoire recorded at Pennine Studios, Oldham, later included on Farrow's compilation album Who Says There's No Beach in Stockport. He attracted more musical attention in 1977, when, as Martin Zero, he produced the first independent punk record, Buzzcocks' Spiral Scratch EP. Under the same moniker he produced early records by punk poet John Cooper Clarke, whose Salford monotone was complemented by drum machines, simple synthesiser motifs and Hannett's bass playing. Jilted John's first single (Jilted John) was Hannett's first hit single.
Hannett became closely associated with Joy Division; Hannett's production incorporated looping technology to treat musical notes with an array of filters, echoes and delays. Hannett had a collection of BBD echo devices which he had amassed and called his "bluetop echo and delay boxes". The first synthesizers Hannett and Joy Division guitarist Bernard Sumner used were Transcendent 2000s and then ARP Omnis. Hannett also owned and used several Jen SX1000s and an International 4600 synthesiser modular synth on many early recordings. Later in his career he owned a Minimoog and several ARP 2600 synths.
Legend has it that he once forced Joy Division drummer Stephen Morris to take apart his drum kit during a recording session and reassemble it, with parts from a toilet. He reputedly had Morris set up his kit on a first floor flat roof outside the fire escape at Cargo Recording Studios, Rochdale. The studio was used for the recording of Digital, Glass, Atmosphere, Dead Souls and Ice Age. Hannett's unorthodox production methods resulted in drum sounds mixed with synthesisers that were complex and highly distinctive. According to Hannett: "There was a lot of space in sound. They were a gift to a producer, because they didn't have a clue. They didn't argue. A Factory Sample was the first thing I did with them. I think I'd had the new AMS delay line for about two weeks. It was called 'Digital'. It was heaven sent."