Bradwell's rule was simple: every actor had to play a musical instrument. The company devised its own work in the rehearsal room rather than performing scripts written elsewhere, an approach that put Hull Truck at the radical edge of 1970s alternative theatre. Bradwell described the goal as 'provocative and challenging, but above all, entertaining,' with an underlying sense of anarchy. The early shows toured out of the Coltman Street house to working men's clubs, late-night cabaret venues, and arts centres. Some of the most successful work was for children. In 1974 the company devised The Knowledge, and although over half the audience walked out of the Manchester premiere, the Guardian's Robin Thornber wrote a rave review that brought the Bush Theatre in London calling. London is where Bradwell would later become artistic director, but Hull Truck was where the company found itself first.

In April 1983 the company moved into the Spring Street Theatre, a 150-seat space converted from St Stephen's church hall (the church itself had been bombed flat during the war). The next year, a 27-year-old former teacher named John Godber took over as artistic director, not entirely aware of how broke the company actually was. Godber turned out to be one of the most prolific playwrights of his generation. His first major play for Hull Truck was Up 'n' Under in 1984, a comedy about amateur rugby league set in Hull's working-class culture. Then came Bouncers, his ferocious 1977 play about nightclub doormen, which became Hull Truck's calling card. Bouncers has been performed somewhere in the world almost continuously for nearly fifty years. Godber stayed twenty-six years, until the company moved to its new building on Ferensway in 2009.

When Hull was named UK City of Culture for 2017, Hull Truck delivered what it called the Year of Exceptional Drama programme. The theatre collaborated with the Royal Shakespeare Company, with Barrie Rutter's Northern Broadsides, and with the Market Theatre of Johannesburg, bringing work from across the world to Hull and sending Hull's work outward. They won the Welcome to Yorkshire White Rose Awards' Arts and Culture prize in 2015, 2017, and 2019, an unprecedented three-time sweep. In 2018 the company hit a controversy when an affiliated artist cancelled their planned production of Ununited Kingdom, a play about far-right politics, after the London staging fell through. The episode underlined how seriously Hull Truck's work was being taken nationally, even when it did not happen.

In March 2022, exactly fifty years after Bradwell placed his Time Out ad, a blue plaque went up on the original Coltman Street house where the company had begun. By then the founding Truckers had scattered: Bradwell to direct the Bush Theatre in London, Steve Halliwell to play Zak Dingle in Emmerdale for twenty-six years, Alan Williams and Rachel Bell to long acting careers. They reunited at Hull Truck in 2012 to perform excerpts from those early shows for the company's fortieth anniversary, the original devisers playing their original parts. The new theatre on Ferensway, with its 440-seat main house and studio space, looks nothing like the church hall on Spring Street and even less like the terraced house on Coltman Street. But the rule still holds. Hull Truck makes work that is provocative, challenging, and entertaining, with an underlying sense of anarchy.