Edmund Anscombe was born on 8 February 1874 in Lindfield, Sussex, England, the son of Eliza Mason and her husband, Edmund Anscombe, a carpenter. The family emigrated to New Zealand when Edmund was seven months old. They settled in Dunedin, where he later attended Caversham School. In 1888 he visited the Centennial International Exhibition, Melbourne, an experience that started a lifelong interest in the design of international exhibitions.
Anscombe served an apprenticeship as a carpenter at Waiwera South. There he met Douglas Watt, whom he married in Kaihiku on 24 May 1898. In 1901 he left New Zealand to study architecture in the United States. It is believed he studied by correspondence and supported himself as a builder – he was engaged in the construction of the Louisiana Purchase Exposition in St Louis, Missouri. The beaux-arts style, on which this exhibition was based, had a considerable influence on Anscombe's later designs.
In 1907 Anscombe returned to Dunedin and in January 1908 won the design competition for the School of Mines building at the University of Otago. In the same year he became an associate of the New Zealand Institute of Architects. The success of the School of Mines building led to his appointment as architect to the university council, a position he held until 1929. The five buildings he designed at the university all faithfully followed the style of Maxwell Bury's original two buildings. Together the seven buildings constitute a major example of nineteenth century and early twentieth century Gothic architecture in New Zealand.
In Otago, Anscombe gained commissions for several major buildings including Otago Girls' High School, Palmerston town hall, the Dunedin YMCA building, and churches of various denominations. He went into partnership with L. D. Coombs in 1913 and then with H. McDowell Smith in 1914. The latter partnership continued in various forms through to the 1920s and received commissions from as far afield as Invercargill and Palmerston North. One of note, undertaken by Anscombe, was for the 33-roomed Clifton homestead at Waiwera South in 1919. Anscombe also supervised the work on the Sarjeant Gallery, Wanganui. His pupil Donald Hosie had won the competition to design the building in 1916, but was killed in the First World War.
In 1919 Anscombe published Modern industrial development, a pamphlet anticipating an era of great prosperity founded on a socialist approach to housing and industrial parks. His vision of commercial buildings with large flat roofs available for recreation purposes and for use as emergency hospitals was not realised until 1937, when he designed the Post and Telegraph Department offices in Herd Street, Wellington.
Anscombe was also able to advance his theories of industrial construction with the development in 1920 of cellular concrete blocks, marketed as the OK Dry Wall System. The blocks were used in the government housing scheme at Miramar, Wellington, and later in R. & W. H. Symington and Company's factory in Palmerston North. They were distributed in Australia.
Following a tour of Canada and the United States in 1922, Anscombe wrote to Dunedin's Evening Star with a proposal to hold an international exhibition in the city. There was overwhelming public support for the project and Anscombe was appointed the official architect. The buildings he designed for the 1925–26 New Zealand and South Seas International Exhibition were structured to an axial plan, terminated by a domed meeting hall. They were greatly influenced by the 1893 World Columbian Exposition, Chicago, and by the 1904 Louisiana Purchase Exposition.
For various reasons Anscombe's involvement in the exhibition was not a happy one. His wife, Douglas, died during the planning stages in 1923. He undertook to organise the amusements, chiefly at his own expense, to ensure the exhibition's success. He believed he was not given due credit for being both 'Originator and Architect' of the exhibition. In 1928 he vented his dissatisfaction by publishing The inside history of the New Zealand & South Seas International Exhibition, Dunedin, 1925–26. He left Dunedin in 1929 and established a practice in Wellington with an office in Hastings.
Anscombe was much influenced by new developments in architecture, and his frequent overseas trips ensured he was always at the forefront of stylistic fashion. After he moved to Wellington his design work became simpler, reflecting the industrial qualities he was writing of in 1919. He also designed several buildings in the Spanish mission style. His more significant structures of the 1930s included the Wellington Show Association stadium, the Hawke's Bay Farmers' and Westerman and Company's buildings in Hastings, and the Rotorua municipal building. He also designed several apartment blocks in Wellington and the Disabled Servicemen's Vocational Training Centre, which was completed in 1943.
However, his most important work was the New Zealand Centennial Exhibition of 1939–40. The International style conveyed by the structures at Rongotai, Wellington, was intended to reflect New Zealand's progressive approach to the world. As an architect of exhibitions Anscombe had the ability and experience to put grand ideas into form. After the Centennial Exhibition he continued to promote various visionary schemes.
Anscombe was well known in the architectural community, as much for his assertive nature as for his prolific designs. He liked to recount how he was dining in the Farmers' building when the 1931 Hawke's Bay earthquake occurred, but, convinced that the architect should have complete faith in his work, he continued eating, undeterred by the violent shakes. Fortunately for Anscombe the building was one of the few that survived.
Although he maintained that work was his hobby, Anscombe played golf and bowls and belonged to the Wellington Savage Club and the local beautifying society. He died in Wellington on 9 October 1948, survived by two daughters.