William Barnett Armson was born in London, England, probably in 1832 or 1833. He was the son of Jane Barnett and her husband, Francis William Armson, a surveyor and builder and later an architect. The Armson family is thought to have arrived in New Zealand in 1852, leaving two years later for Melbourne, Australia. There William began his architectural training with the firm of Russell, Watts and Pritchard, followed by five years with Purchas and Swyer. The principal elevation of a richly modelled Italian Renaissance palazzo for the Bank of Australasia ( c. 1860–61), and a design for a gold case, signed 'W. B. Armson, Architect' and dated May 1861, are among his earliest surviving drawings and indicate that he was by this time in independent practice. The meticulous draughtsmanship they displayed was to be a hallmark of his work.
In March 1862 Charles Swyer was recruited to the position of engineer to the Otago provincial government in New Zealand. Armson arrived in Dunedin shortly after Swyer, on 1 April, initially to practise on his own account, but within three weeks he had secured an appointment as draughtsman in the provincial engineer's department. Two months later he was promoted to assistant architect. He spent two years with the department, and his signature appears alongside Swyer's on surviving plans. During this time he was supporting his widowed mother in Melbourne. He is said to have predicted that he would die, like his father and grandfather, at the age of 50. He was never to marry.
In June 1864 retrenchment in the provincial government administration saw Armson given two months' notice, and he resumed private practice. Towards the end of the year he undertook to supervise the construction of St Luke's Church, Ōamaru, to a design by his former colleague in the provincial engineer's department, Edward Rumsey. By January 1865 the firm of Thornley and Armson was advertising its services in Ōamaru as 'Architects, Civil Engineers, Surveyors and Land and Estate Agents'. After completing the first stage of St Luke's, however, in December Armson sailed on the South Australian for Melbourne. When he returned to New Zealand early the following year he settled in Hokitika.
On the West Coast Armson carved out a successful career as an architect, engineer and surveyor, working as town surveyor to the Hokitika Municipal Corporation while maintaining a steady private architectural practice. He designed branch offices for the Union Bank of Australia in Hokitika, Waimea (Goldsborough) and Greymouth, the Bank of Australasia (Hokitika and Greymouth), and the Bank of New South Wales (Greymouth and Ross), and other commercial premises such as hotels and shops. He also designed cottages, and churches at Ross and Greymouth. His finest work in this period was the Hokitika Town Hall (1869), its facade of richly modelled Renaissance classical motifs giving an appearance of masonry which belied the fact that it was built of timber, like much of his West Coast work. None of Armson's timber buildings have survived.
The most productive and successful phase of Armson's career dates from November 1870, when he settled in Christchurch. Most of his work there was for commercial enterprises; in Hereford Street alone he completed 14 major contracts. Although most of these buildings were classical Italianate in style, he also produced designs in the fashionable northern Italian Gothic. His only surviving work in Hereford Street, the Fisher building, is an example of the latter. Other commercial buildings were Italian Renaissance or Palladian in inspiration: for example, Anderson's building in Cashel Street; the Shamrock Hotel, Manchester Street; Butterworth Brothers' building in Lichfield Street; and the New Zealand Loan and Mercantile Agency Company store in Moorhouse Avenue, all built in 1881.
Among Armson's public buildings in Christchurch are several Gothic designs: the former public library (1875), the original Christchurch Boys' High School (1879), and the former Christchurch Girls' High School in Cranmer Square (1880). The nave of St Mary's Church, Timaru, begun in 1880, was also built to his design. From Christchurch Armson also designed bank offices for a number of other towns. These range from relatively simple timber structures for the Bank of New Zealand in Temuka (1875) and Rakaia (1881), to the elaborately ornamented Bank of New South Wales in Auckland (1882), long since demolished.
The Bank of New Zealand in Dunedin, begun in 1879, is Armson's grandest and finest work. His contemporaries regarded it as 'one of the most perfect of its kind in the Southern Hemisphere', unrivalled 'for purity and richness of design'. A lavish essay in Venetian high Renaissance, reminiscent of gentlemen's club buildings in Pall Mall, London, the bank was also his monument: he did not live to see its completion. He died at Christchurch on 25 February 1883, aged 50.
William Armson operated at a level of professionalism rare in New Zealand at that time. In 1881 he employed a staff of 13. He was a co-founder of the Canterbury Association of Architects in 1871 or 1872, and was also a foundation member of the Canterbury Club. A pupil recalled him as being 'afraid of no-one, and meticulous about his professional standing'. His correspondence with officialdom, clients and workmen could be exceedingly brusque. The 'short, tubby and slightly bald' Armson commanded respect and admiration, however, not only for the quality of his work but also for his convivial and generous nature.