Walter H. Cobley was an articled pupil of the civil engineer Alfred Williams in London, and after qualifying worked in the Engineer's Department of the Taff Vale Railway, at Cardiff, Wales. He became a member of the (British) Institution of Civil Engineers. In February 1876 he was appointed as assistant engineer in the Natal Government Railways, arriving in Natal on 13 March. He subsequently served as acting maintenance engineer from January 1880; maintenance engineer from May 1882; district engineer, construction, from January 1883; district engineer, maintenance, from January 1887; and district engineer, border extension (Charlestown to border, and District No. 1, Charlestown-Johannesburg railway) from March 1894. In July 1897 he became superintending engineer of surveys and construction in Pietermaritzburg, a post he held until 1908. After 1900 he directed a survey for a possible alternative main line from the base of Biggarsberg to the mouth of the Umgeni River at Durban, a distance of 293 km. However, the line was not built. In 1903 he was awarded the Imperial Service Order (ISO), a decoration for long and meritorious service in the British civil service in a clerical or administrative capacity.
Cobley compiled two maps of Natal. The first, in 1900, on a scale of one mile to the inch (1:63 360); the second, in 1905, on a scale of 16 miles to the inch (1:1 013 760). Both are in the Natal Archives, Pietermaritzburg. He also had a hand in the compilation of many maps of railway surveys in Natal.
Cobley became a founding member of the South African Association for the Advancement of Science in 1902, and was still a member in 1906. He was married to Annie Barker, with whom he had one son and three daughters.