John Henry Brady was a mathematics exhibitioner at Queen's College, Oxford, and was awarded the degree Bachelor of Arts (BA), though his qualification is sometimes listed as Master of Arts (MA). In September 1880 he was appointed assistant lecturer at the Diocesan College, Cape Town. The next year he was admitted to the BA degree by the University of the Cape of Good Hope on the basis of his British qualifications. From July 1882 to October 1883, and again from March to September 1890, he served as acting registrar of the university, in the absence of the registrar, James Cameron*. He also served the university as an examiner in literature (1884) and French (1888).
In November 1883 Brady was appointed deputy inspector of colleges and schools in the Department of Education of the Cape Colony. This appointment was changed to deputy inspector of schools in 1884. In September 1889 he became assistant superintendent-general of education for the Cape Colony, and in March 1893 registrar and deputy inspector of schools - the most senior post under the superintendent-general of education, Thomas Muir*. He filled this post to 1897, when he left the civil service.
Brady was active in natural history, and particularly entomology, from at least 1888. In March that year he delivered a long lecture on the eye as an optical instrument to the Eastern Province Naturalists' Society during one of several visits to Port Elizabeth. Already at this time a species of locust, Porthetis bradyana, had been named after him and he was described as specialising in some groups of the Coleoptera (beetles). During 1889, though living in Cape Town, he donated 48 species of insects to the Port Elizabeth Museum and provided help with the arrangement of its collections. During this year he also donated 130 species of Coleoptera in a good state of preservation to the Albany Museum in Grahamstown. He followed this up with more beetles in 1891, and with a large collection of 3457 specimens, both South African and foreign, in 1895. During the next year a set of beautiful tropical Lepidoptera was acquired from him "at nominal cost" by the Albany Museum. Following his death in 1903 his wife donated his entomological books and his whole collection of 7000 Coleoptera to the Albany Museum before returning to England. This collection, together with his earlier donations of foreign insects, was to form the Brady Memorial Collection of Foreign Insects.
Brady was a member of the South African Philosophical Society from 1892, but not for long.