Blackett married Constanza Bayon (1899–1986) in 1924. They had one son and one daughter.
In August 1914 on the outbreak of World War I Blackett was assigned to active Service as a midshipman. He was transferred to the Cape Verde Islands on HMS Carnarvon and was present at the Battle of the Falkland Islands. He was then transferred to HMS Barham and saw much action at the Battle of Jutland. While on HMS Barham, Blackett was co-inventor of a gunnery device on which the Admiralty took out a patent. In 1916 he applied to join the RNAS but his application was refused. In October that year he became a sub-lieutenant on HMS P17 on Dover patrol, and in July 1917 he was posted to HMS Sturgeon in the Harwich Force under Admiral Tyrwhitt. Blackett was particularly concerned by the poor quality of gunnery in the force compared with that of the enemy and of his own previous experience, and started to read science textbooks. He was promoted to Lieutenant in May 1918, but had decided to leave the Navy. Then, in January 1919, the Admiralty sent the officers whose training had been interrupted by the war to Cambridge University for a course of general duties. On his first night at Magdalene College, Cambridge he met Kingsley Martin and Geoffrey Webb, later recalling that he had never before, in his naval training, heard intellectual conversation. Blackett was impressed by the prestigious Cavendish Laboratory, and left the Navy to study mathematics and physics at Cambridge.
After graduating from Magdalene College in 1921, Blackett spent ten years working at the Cavendish Laboratory as an experimental Physicist with Ernest Rutherford and in 1923 became a fellow of King's College, Cambridge, a position he held until 1933.
Blackett spent some time in 1924–1925 at Göttingen, Germany working with James Franck on atomic spectra. In 1932, working with Giuseppe Occhialini, he devised a system of geiger counters which only took photographs when a cosmic ray particle traversed the chamber. They found 500 tracks of high Energy cosmic ray particles in 700 automatic exposures. In 1933, Blackett discovered fourteen tracks which confirmed the existence of the positron and revealed the now instantly recognisable opposing spiral traces of positron/electron pair production. This work and that on annihilation radiation made him one of the first and leading experts on anti-matter.
In 1935 Blackett was invited to join the Aeronautical Research Committee chaired by Sir Henry Tizard. The committee was effective pressing for the early installation of Radar for air defence. In the early part of World War II, Blackett served on various committees and spent time at the Royal Aircraft Establishment (RAE) Farnborough, where he made a major contribution to the design of the Mark XIV bomb sight which allowed bombs to be released without a level bombing run beforehand. In 1940–41 Blackett served on the MAUD Committee which concluded that an atomic bomb was feasible. He disagreed with the Committee's conclusion that Britain could produce an atomic bomb by 1943, and recommended that the project should be discussed with the Americans. He was elected a Fellow of the Royal Society (FRS) in 1933 and awarded its Royal Medal in 1940.
That same year he moved to Birkbeck College, University of London as Professor of Physics for four years. Then in 1937 he went to the Victoria University of Manchester where he was elected to the Langworthy Professorship and created a major international research laboratory. The Blackett Memorial Hall and Blackett lecture theatre at the University of Manchester were named after him.
Blackett became friends with Kingsley Martin, later Editor of the New Statesman, while an undergraduate and became committed to the left. Politically he identified himself as a socialist, and often campaigned on behalf of the Labour Party. In the late 1940s, Blackett became known for his radical political opinions, which included his belief that Britain ought not develop atomic weapons. He was considered too far to the left for the Labour Government 1945-1951 to employ, and he returned to academic life. His internationalism found expression in his strong support for India. There in 1947 he met Jawaharlal Nehru, who sought his advice on the research and development needs of the Indian armed forces and for the next 20 years he was a frequent visitor and advisor on military and civil science. These visits deepened his concern for the underprivileged and the poor. He was convinced that the Problem could be solved by applying science and Technology and he used his scientific prestige to try and persuade Scientists that one of their first duties was to use their skill to ensure a decent life for all mankind. Before underdevelopment became a popular issue he proposed in a presidential address to the British Association that Britain should devote 1% of its national income to the economic improvement of the third world and he was later one of the prime movers in the foundation of the Overseas Development Institute. He was the senior member of a group of Scientists which met regularly to discuss scientific and technological policy during the 13 years when the Labour Party was out of office, and this group became influential when Harold Wilson became leader of the Party. Blackett's ideas led directly to the creation of the Ministry of Technology as soon as the Wilson government was formed and he insisted that the first priority was revival of the computer industry. He did not enter open politics, but worked for a year as a civil servant. He remained deputy chairman of the Minister's Advisory Council throughout the administration's life, and was also personal scientific adviser to the Minister.
In 1947, Blackett introduced a theory to account for the Earth's magnetic field as a function of its rotation, with the hope that it would unify both the electromagnetic force and the force of gravity. He spent a number of years developing high-quality magnetometers to test his theory, and eventually found it to be without merit. His work on the subject, however, led him into the field of geophysics, where he eventually helped process data relating to paleomagnetism and helped to provide strong evidence for continental drift.
In 1948 he was awarded the Nobel Prize in Physics, for his investigation of cosmic rays using his invention of the counter-controlled cloud chamber.
Professor Blackett was appointed Head of the Physics Department of Imperial College London in 1953 and retired in July 1963. The current Physics department building of Imperial College is named the Blackett Laboratory.
Blackett had refused many honours in the manner of a radical of the twenties but accepted a Companion of Honour in the 1965 Birthday Honours, and was appointed to the Order of Merit in 1967. He was created a life peer on 27 January 1969 as Baron Blackett, of Chelsea in Greater London. However, the greatest honour of all for him was when he was made President of the Royal Society in 1965. The crater Blackett on the Moon is named after him.
In 2016, the house that Blackett lived in from 1953 to 1969 (48 Paultons Square, Chelsea, London) has received an English Heritage Blue Plaque