During World War II, he initially worked on radar in Suffolk, then with Cecil Powell in Bristol on a project that attempted to use photographic methods to detect fast particles from radioactive decay. James Chadwick recruited him to a Cambridge University team working on a possible heavy water reactor. The team was part of the British Tube Alloys directorate which was merged into the American Manhattan Project, the successful effort to create a nuclear weapon. In January 1943 the Cambridge team including Nunn May transferred to the Montreal Laboratory which was building a reactor at Chalk River near Ottawa, Canada.His Canadian job ended in September 1945, and he returned to his lecturing post in London.
He had let his membership of the Communist Party lapse by 1940, but at Cambridge when he saw an American report mentioning that Germany might be able to build a dirty bomb he passed this on to a Soviet contact. In Canada he was approached by Lt Angelov of the GRU (Soviet military intelligence) for information on atomic research. He secretly supplied microscopic samples of the isotopes Uranium-233 and 235, and also borrowed library research documents on nuclear power, many from the USA, for copying. The Canadian Royal Conmmission said he was paid with two bottles of whisky and at least $700 (Canadian); Nunn May said he accepted the money under protest and promptly burnt it. Angelov gave him details for a rendezvous with the GRU next to the British Museum in London after his return.
When a KGB officer in Canada, Igor Gouzenko defected to the West, he passed along copies of GRU documents including details of the proposed meeting in London. Nunn May did not go to the Museum meeting, but he was arrested in March 1946. Nunn May confessed to espionage. On 1 May 1946, he was sentenced to ten years hard labour. He was released in 1952, after serving six and a half years. After his release, he characterized his passing Uranium isotopes to the Soviet Union as a "contribution ... to the safety of mankind."
Blacklisted from universities in Britain, Nunn May worked for a scientific instruments company, then in 1961 went to work at the University of Ghana, where he conducted research in solid state physics and created a science museum.
He died of pneumonia and pulmonary disease. A 2002 statement released after his death stated that he had no regrets about his spying activities.
His arrest and sentence in 1946 first showed publicly that the Soviet Union had obtained atomic secrets by espionage. His clearance by MI5 also led to American distrust of Britain, and the McMahon Act. He passed on information on atomic reactors, but unlike Klaus Fuchs (who was arrested in 1950) he knew little of weapon design.