Peter was born on June 3, 1917 in Australia. He received a bachelor of science degree in physics in 1939 from the University of Melbourne. During the Second World War he worked at the Munitions Supply Laboratories until 1942 and then at the Amalgamated Wireless company in Sydney. In 1944, he began graduate studies at the University of Sydney where he completed his Master's thesis on a study of high frequency fields in an ionized gas. He then entered Oxford University in the UK, where he received his doctoral degree.
At Oxford, he carried out the first studies of toroidal discharges in which a current is induced to travel in a ring around a "doughnut-shaped" tube. This led to his becoming head of fusion research effort at Oxford. The UK fusion effort, thus born at Oxford, moved to the government's Harwell laboratory in 1952 where it continued in secret. The ZETA device, based on Thonemann's work Oxford, was designed and built at Harwell and began operation in 1957. The UK successfully tested it first hydrogen bomb the same year. ZETA continued to operate at Harwell until 1969 and its results let to the Reversed Field Pinch (RFP) concept.
Following declassification of fusion research internationally at the 2nd UN Conference on the Peaceful Uses of Atomic Energy in 1958, UK fusion research was transferred to a new laboratory at Culham, south of Oxford. Thonemann served as deputy director of the Culham Laboratory 1965-66 and left the laboratory in 1968 to become Professor of Physics at the University College of Swansea, Wales. He retired from Swansea University in 1984.