Henry Louis Langley Feltham, son of Henry J. Feltham, came to the Cape Colony as a child in 1866. He was educated at the Diocesan College in Cape Town and after matriculating in 1877 was awarded the degree Bachelor of Arts (BA) by the University of the Cape of Good Hope in 1879. He continued his studies at Trinity Hall, Cambridge, where he qualified in law. Upon his return to the Cape Colony he was admitted as an advocate in 1884 and practised as such in Kimberley from 1884 to 1888. In 1893 he moved to Johannesburg, joined the firm of Charles Leonard, and two years later married Annie C. Guest. In 1899 he was living in Kenilworth, Cape Town, but soon returned to Johannesburg where he remained to become a partner in the firm Van Hulsteyn, Feltham & Fry* (later Van Hulsteyn, Feltham & Ford). He was still a senior partner in the firm by 1927.
Feltham was an avid collector of Lepidoptera (butterflies and moths). He collaborated with Roland Trimen* at the South African Museum in Cape Town, but also built up a private collection. Trimen, in the preface to his book South African butterflies... (1887-1889) thanked him for presenting a small collection of butterflies from Griqualand West, with notes of much interest, showing that Feltham started collecting during his stay in Kimberley in the 1880s. In 1893 he presented some more butterflies from Kimberley and Johannesburg to the South African Museum. These were followed in 1900 by a further donation of Lepidoptera from the same places and from Cape Town, including many moths new to the museum's collections. By 1904 he seems to have been back in the Transvaal, for during 1903/4 he donated a collection of Cape Lepidoptera to the Transvaal Museum, all of which were new to the museum's collection. He followed this up with a further donation of Cape butterflies the next year, most of which were also new to the museum. In 1912 the Director of Albany Museum, J. Hewitt*, sent him some specimens for identification and described him as "the leading authority on the South African butterfly fauna". By 1919 A.J.T. Janse believed that Feltham had the best private collection of lepidoptera in the country. The collection was acquired by the University of the Witwatersrand before 1940, while his papers, including field notes on butterflies, are housed in the university's library.
Feltham became a member of the South African Philosophical Society in 1899 and remained a member of its successor, the Royal Society of South Africa, to at least 1917. He was a foundation member of the South African Ornithologists' Union in 1904, and by 1920 was still a member of its successor, the South African Biological Society. He was also president of the Johannesburg Field Naturatists Club. At some time he was elected a Fellow of both the (British) Entomological Society and the Zoological Society of London.