During World War II, Adams worked in the Radar laboratories of the British Ministry of Aircraft Production where he learned physics and engineering on the job. After the war he moved to Harwell and the Atomic Energy Research Establishment. He had no formal qualifications but became expert in the design and construction of the advanced machines and instruments used in physics research, designing a 180 MeV synchro-cyclotron. In 1953 he joined CERN as director of the Proton Synchotron division. In 1961 he returned to the UK as director of the Culham Fusion Laboratory, and then from 1966 to 1971 he was a member of the United Kingdom Atomic Energy Authority.
Returning to CERN in 1971 as Director-General of Laboratory II, he led the design of the Super Proton Synchrotron. He split the duties of CERN Director General with Willibald Jentschke and then Léon van Hove during the 1970s. With the reorganisation of CERN in 1976 he became the executive Director-General, working on obtaining funding for the LEP collider.