The Workshop was set-up to satisfy the growing demand in the late 1950s for "radiophonic" sounds from a group of producers and studio managers at the BBC, including Desmond Briscoe and Daphne Oram. For some time there had been much interest in producing innovative music and sounds to go with the pioneering programming of the era, in particular the dramatic output of the BBC Third Programme.

One of the few benefits of wartime had been that some women had an opportunity to work in jobs previously denied to them; Daphne Oram was one. Daphne had started working for the BBC as a 'music balancer' during the war, turning down a place at the Royal College of Music to do so. After her promotion to studio manager in the '50s, she began pestering the BBC to follow the lead of the French broadcasters, and to provide a facility for the production of electronic sound and musique concrète. Desmond Briscoe (1925-2006) was also a studio manager, with similar interests, so in 1957 the pair teamed up to produce some innovative programmes for the BBC Drama Department. Using borrowed test oscillators and tape-splicing techniques, they produced sounds that had never been heard before on the BBC.

Often the sounds required for the atmosphere that programme makers wished to create were unavailable or non-existent through traditional sources and so some, such as the musically trained Oram, would look to new techniques to produce effects and music for their pieces. Much of this interest drew them to musique concrète and tape manipulation techniques, since using these methods could allow them to create soundscapes suitable for the growing range of unconventional programming. When the BBC noticed the rising popularity of this method they established a Radiophonic Effects Committee, setting up the Workshop in rooms 13 & 14 of the BBC's Maida Vale studios with a budget of £2,000. The Workshop regularly released technical journals of their findings - leading to some of their techniques being borrowed by sixties producers and engineers such as Eddie Kramer.

Their nagging finally paid off, and in April 1958 Desmond and Daphne founded the Radiophonic Workshop in the BBC's Maida Vale Studios (a former ice-skating rink). They were joined later in the year by 'technical assistant' Dick Mills. Brian Hodgson came along in 1962 and he eventually ended up running the place. Brian adds: "Workshop was then a very popular word among theatre 'types', and it gave away the Drama Department origins. It was originally going to be called the Electrophonic Workshop, but it was discovered that 'electrophonic' referred to some sort of defect of the brain, so it had to be changed! A board was set up to see that the place was run properly. Unfortunately, one board member had a doctor friend, who advised that three months should be the maximum length of time that anyone could work there, as staying any longer could be injurious to their health; they'd go mad, or something. This problem recurred throughout the Workshop's history — just as a recruit was getting into the swing of things, they'd have to leave."

Daphne Oram was the first to fall foul of this rule. After three months in her new job, she was ordered back to work in a control room at Broadcasting House. But for some reason Desmond Briscoe was not required to leave: instead he was appointed as the Workshop's Senior Studio Manager. For the BBC's women, it seemed, the war was over. A lengthy and bitter row ensued, and eventually, Daphne left the BBC for good in 1959, moving to an oast-house that she'd bought in Kent and establishing her own Oramics Studios for Electronic Composition. She was replaced by Maddalena Fagandini.

In 1958, Desmond Briscoe was appointed the Senior Studio Manager with Dick Mills employed as a technical assistant. Much of The Radiophonic Workshop's early work was in effects for radio, in particular experimental drama and "radiophonic poems". Their significant early output included creating effects for the popular science-fiction serial Quatermass and the Pit and memorable comedy sounds for The Goon Show. In 1959, Daphne Oram left the workshop to set up her own studio, the Oramics Studios for Electronic Composition, where she eventually developed her "Oramics" technique of electronic sound creation. That year Maddalena Fagandini joined the workshop from the BBC's Italian Service.

From the early sixties the Workshop began creating television theme tunes and jingles, particularly for low budget schools programmes. The dramatic move from the experimental nature of the late 50s dramas to the cheery themes was noticeable enough for one radio presenter to have to remind listeners that the purpose of the Workshop was not pop music. In fact, in 1962 one of Fagandini's interval signals "Time Beat" was reworked with assistance from George Martin (in his pre-Beatles days) and commercially released as a single using the pseudonym Ray Cathode. During this early period the innovative electronic approaches to music in the Workshop began to attract some significant young talent including Delia Derbyshire, Brian Hodgson and John Baker, who was in fact a jazz pianist with an interest in reverse tape effects.

In these early days, one criticism the Workshop attracted was its policy of not allowing musicians from outside the BBC to use its equipment, which was some of the most advanced in the country at that time not only because of its nature, but also because of the unique combinations and workflows which the Workshop afforded its composers. In later years this would become less important as more electronic equipment became readily available to a wider audience.