His key works include the 1925–26 New Zealand and South Seas International Exhibition, the 1940 New Zealand Centennial Exhibition, the Herd Street Post and Telegraph building, Anscombe Flats, the Empire Deluxe theatre and his work on the clocktower complex – including specifically the Archway Building and Marama Hall – effectively re-conceiving the design of the University of Otago's historical core (University of Otago Clocktower complex).

His parents Edmund and Eliza Anscombe (née Mason) emigrated on 27 June 1874 to New Zealand on the Christian McAusland in the assisted immigration scheme.

Whether the exhibition was the primary reason for his visit to Melbourne cannot be known for certain, but on his return Anscombe became an apprentice carpenter in Waiwera South, Otago, and worked for his father as a builder.

He visited St Louis Purchase Exposition where he "received ... practical training in exhibitions in 1904" and it is during this time that he is said to have studied architecture, an idea first asserted in an obituary but something Anscombe himself does not refer to.

Described as "an architect now resident in Dunedin, who has had considerable experience in the United States," Anscombe won the University of Otago School of Mines competition in 1907 under the pseudonym: "Esperanto."

Anscombe's early and consistent success in competitions (which included: the School of Mines (1907), Hanover Street Baptist Church, Dunedin (1912), Y.M.C.A.

Anscombe's practice continued to flourish and commissions from this time included the Maheno and Marama Hospital Ships' Surplus Fund Memorial Hall (1919/1923), the Lindo Ferguson Building (1927), the University of Otago Dental School (1924), Arthur Barnett's Department Store (1924), now part of the Meridian Mall, Dunedin, Messers Herbert, Haynes and Co Ltd building (1925), Logan Park Grandstand (1929) and, of course, the design work for the New Zealand and South Seas International Exhibition (1925–26), including the still surviving art exhibition building (1924), which involved a number of overseas trips specifically to Melbourne to consult with the engineer of the scenic railways in Melbourne.

offer of a "donated" plan which, it seems, fast became conditional on the assurance of further work and he described this as "decidedly infra dig and a breach of etiquette on the part of ... the Institute much to be regretted."

In 2024, a house built by Anscombe at 284 Stuart Street, opposite the Mandeno-designed King Edward Technical College, was threatened by demolition, along with a protected lime tree on the site.

They left for this trip in early March 1928 and travelled to the Middle East (Egypt, Greece, Palestine, and Turkey), Britain (England, and Ireland), and Europe (Austria, Belgium, Czechoslovakia, France, Germany, Italy, Switzerland) concluding the journey in America before returning to New Zealand via Honolulu and Suva.

The Anscombe's occupied the penthouse flat at Lyndfield, which, when his daughters married and left home, became a place of regular extended family gatherings.

The flat was also where Anscombe trialled drafts of his schemes, letters, and proposals in front of his architect sons-in-law, daughters and grandchildren for discussion and feedback.

Anscombe employed a small office in Wellington which designed a range of work including residential apartments (Lyndfield and Olympus on Oriental Parade, Franconia on The Terrace (1938), Belvedere at the corner Austin and Majoribanks Streets), Hamilton Flats (Hawker Street) and commercial and institutional projects including: the Post and Telegraph Building, Herd St (1939), Dominion Motors, the Island Bay kindergarten, and the Lloyd St, Disabled Soldiers' Vocational Centre (1943).

In 1929 Anscombe was commissioned by the Hawke's Bay Farmer's Cooperative Association to design a new head office following a disastrous fire that destroyed their building in 1928.

[5][6] The building was of a strong Stripped Classical design constructed to withstand earthquakes due to its floating foundations, meaning it would not strain with tension of ground movement.

When the quake stopped, most of the Hastings central business district had collapsed or was badly damaged, except for Anscombe's building, and as a result no lives were lost.

[6]The building commands a prominent position in the Russell Street Historic Area of Hastings and is iconic for its highly decorative below verandah façade with original Wunderlich pressed metal soffits, terrazzo panelling, bronzed-copper window joinery, bevelled glass and leadlight.

On this same trip he visited Long Beach, California where he was ""very impressed with the beautiful waterfront feature enclosing an area of 32 acres (130,000 m2) of still water.""

This influenced his 1945 proposal for a bandshell and amenities on a 20-foot (6.1 m) wide promenade wall to enclose 10 acres (40,000 m2) of still water with an illuminated fountain at Oriental Bay, published in The Evening Post in February 1945.

In early May 1940, Anscombe anticipated travel to America and wrote to the Minister of Supply, Dan Sullivan, that he was "anxious to visit the United States shortly – primarily to visit both the San Francisco and New York Worlds Fairs – but while there I intend to check up on the latest development in Combined Factories, Housing, City Planning Schemes generally, Air Port Schemes, Bus Termini Stations etc."

In an article from June 1924, Anscombe outlined a proposal for a highway reserve, a park system, city zoning and housing, influenced by "the park and parkway system of Kansas City" and in keeping with Anscombe's "municipal housekeeping on scientific lines" outlined in his 1915 paper: "The Economic Value of Scientific Town Planning."

The proposal was not implemented exactly as Anscombe suggested yet much of his intention has persisted, including the tree-lined Anzac Avenue and Logan Park, in Dunedin.

This central location was to take advantage of such already existing facilities as Government House, the Public Hospital, Wellington Boys' College, and the Museum and Art Gallery.

Anscombe's next travel overseas was an extensive tour of Canada and the United States where he visited "over fifty Canadian and American cities" in 1922.