Dingle was a member of the British government eclipse expeditions of 1927 (Colwyn Bay) and 1932 (Montreal), both of which failed to make any observations due to overcast skies. He spent most of 1932 at the California Institute of Technology as a Rockefeller Foundation Scholar. There he met the theoretical cosmologist R. C. Tolman, and studied relativistic cosmology.
Dingle became a professor of Natural Philosophy at Imperial College in 1938, and was a professor of History and Philosophy of Science at University College London from 1946 until his retirement in 1955. Thereafter he held the customary title of Professor Emeritus from that institution. He was one of the founders of the British Society for the History of Science, and served as President from 1955 to 1957. He founded what later became the British Society for the Philosophy of Science as well as its journal, the British Journal for The Philosophy of Science.
Dingle was the author of "Modern Astrophysics" (1924) and "Practical Applications of Spectrum Analysis" (1950). He also wrote the essay "Relativity for All" (1922) and the monograph The Special Theory of Relativity (1940). A collection of Dingle's lectures on the history and philosophy of science was published in 1954. He also took an interest in English literature, and published Science and Literary Criticism in 1949, and The Mind of Emily Brontë in 1974.
The second dispute began in the late 1950s, following Dingle's retirement and centered on the theory of special relativity. Initially Dingle argued that, contrary to the usual understanding of the famous twin paradox, special relativity did not predict unequal aging of twins, one of whom makes a high-speed voyage and returns to Earth, but he then came to realize and acknowledge that his understanding had been mistaken. He then began to argue that special relativity was empirically wrong in its predictions, although experimental evidence showed he was mistaken about this. Ultimately Dingle re-focused his criticism to claim that special relativity was logically inconsistent: "The theory [special relativity] unavoidably requires that A works more slowly than B and B more slowly than A --which it requires no super-intelligence to see is impossible." Hence he asserted that the well-known reciprocity of the Lorentz transformation is self-evidently impossible. As Whitrow explained in Dingle's obituary, this is not correct.
Dingle carried on a highly public and contentious campaign to get this conclusion accepted by the scientific community, mostly through letters to the editors of various scientific periodicals, including Nature. Dozens of scientists responded with answers to Dingle's claims, explaining why the reciprocity of the Lorentz transformation does not entail any logical inconsistency, but Dingle rejected all the explanations. This culminated in his 1972 book, Science at the Crossroads in which Dingle stated that "a proof that Einstein's special theory of relativity is false has been advanced; and ignored, evaded, suppressed and, indeed, treated in every possible way except that of answering it, by the whole scientific world." He also warned: "Since this theory is basic to practically all physical experiments, the consequences if it is false, modern atomic experiments being what they are, may be immeasurably calamitous." The consensus in the physics community is that Dingle's objections to the logical consistency of special relativity were unfounded.