Hugh Exton qualified magna cum laude as Doctor of Medicine (MD) at the University of Giessen, Germany, in 1861. He came to the Cape that same year and worked in a homeopathic dispensary in Cape town before setting up practice in Grahamstown. A few years later he went on an adventurous journey to Matabeleland and Tati. In 1868 he undertook a second journey to Matabeleland and present Botswana, where he collected birds and other natural history specimens and gathered information for three articles published in the Cape Monthly Magazine. One of these dealt with "The Bojala, a Bechuanaland ceremony" (1870, pp. 281-289), another with "Notes in natural history" (1871, pp. 218-222) and the third with "The philosophy of birds' nests in relation to instinct" (1871, pp. 342-354). Six birds from "the country beyond the Transvaal" (Grahamstown Journal, 19 May 1869) he presented to the Albany Museum, Grahamstown, followed by another 16 from Kanye, Botswana. Specimens were also sent to the South African Museum in Cape Town. He visited the diamond fields near Kimberley as well, and contributed a letter on their geology to the same journal (1871, pp. 380-382). E.L. Layard* quoted Exton in notes he published on South African birds in The Ibis in 1869 and 1871, and in the latter year named and described Exton's Barbet (Pogoniulus chrysoconus extoni. Exton made notes on the birds he observed in a copy of Layard's Birds of South Africa, and these notes were published by Austin Roberts* in The Ostrich in 1935.
Meanwhile Exton had moved to Bloemfontein in 1870, where he remained for more than thirty years. He was licensed to practise in the Orange Free State in 1870, and later also in the Cape Colony (1880 or 1886) and the Transvaal (1888). Apart from practising medicine in Bloemfontein he involved himself in public affairs. He was a founding member of the Bloemfontein Debating Society in March 1877 (soon renamed the Bloemfontein Literary and Scientific Society). That same year he took an active part in the founding of the National Museum of the Orange Free State, becoming its first honorary curator and donating a number of birds and a collection of birds' eggs from Bloemfontein to its collections. From September 1881 to August 1883 he served as mayor of the town, ending his term of office to go on a visit to England. He remained in London to 1885. In that year he became a licentiate of the Society of Apothecaries, was elected a Fellow of the Geological Society on London, and bought some specimens for the National Museum before returning to Bloemfontein. Once more he became honorary curator of the museum. It was perhaps during this visit that he presented a number of South African fossils to the British palaeontologist Sir Richard Owen*, including the remarkable mammal-like reptile, Tritylodon longaevus. In 1888 Exton succumbed to the prevailing gold fever and moved to Johannesburg, where he showed an interest in geological matters. The short-lived South African Geological Association was formed in Grahamstown that year, with members from all over southern Africa. Exton served on its first council, but the association ceased to function after about two years. When the Geological Society of South Africa was founded in 1895 he was elected its first president, a position he retained until 1902, after the Anglo-Boer War (1899-1902). His inaugural address and two subsequent presidential addresses were published in the societies Transactions (1896, Vol. 1, pp. 1-11; 1897, Vol. 3, pp. 4-8; 1898-1899, Vol. 4, pp. 6-10). He published some minor papers and notes on geological matters, including "Geological notes on the neighbourhood of Ladysmith, Natal" (Geological Magazine, 1901) and wrote an obituary of Dr. W.G. Atherstone* for the Transactions of the Geological Society of South Africa (1898, Vol. 4, pp. 61-65). The next year he again donated some natural history specimens to the Albany Museum, including a sample of aragonite from the recently discovered Sterkfontein Cave.
In 1894 Exton contributed a paper on aphasia, resulting from a depressed fracture of the skull, to the South African Medical Journal. He was a member of the Transvaal Medical Society and served as its president in 1895-1896. At the outbreak of the Anglo-Boer War in October 1899 he left Johannesburg to serve as civil surgeon with the Natal Field Force. He was stationed in Ladysmith Hospital from its relief in 1900 to the declaration of peace in 1902. Just before his death, while living in Port Alfred, he joined the South African Association for the Advancement of Science. Exton had wide intellectual interests and a high sense of duty, and was amiable and courteous in manner. He was one of the corresponding members of the South African Philosophical Society during its early years.