In the early years the practice designed relatively small buildings in and around Bury. Their first major commission came in 1871 for Cambridge Hall, Southport. Later works included the Ulster Reform Club in Belfast, and extensive temporary structures to house the Royal Jubilee Exhibition in Manchester in 1887/1888. After this they had their most notable commission, the design of Blackpool Tower. Both senior partners died before this could be completed, and the work was continued by Frank Maxwell. The commercial success of Blackpool Tower led to a commission to design the even larger New Brighton Tower. The practice continued to design notable buildings into the 20th century.
James Maxwell was born on 14 June 1838 in Haslingden, Lancashire. His father, Thomas, was a builder, plumber and glazier. James was educated at the grammar school in Whalley, and was then articled to Thomas Holmes, an architect in Bury, which was then in Lancashire and later in Greater Manchester. Maxwell established his own architectural practice in Bury in December 1857. On 28 September 1893 he died at his home in Bury from cerebritis.
William Charles Tuke, usually known as Charles Tuke, was born on 12 January 1843 in the village of Bolton in the parish of Calverley near Bradford, West Yorkshire. His father, William, was a land agent, architect, and surveyor. He first trained as an articled clerk in his father's practice, moved briefly to Chester, worked as an architect's assistant in Wolverhampton, and then undertook the same role in the practice of Mills and Murgatroyd in Manchester. Tuke joined Maxwell in 1865 and became his partner in 1867. Tuke later lived at The Hydro, St Annes on Sea, Lancashire, where he died on 28 March 1893 from nephritis.
Francis William Maxwell, usually known as Frank, was the second son of James Maxwell, and was born in Bury on 7 December 1863. He was educated at the Friend's School in Kendal and then at Owen's College, Manchester. In the late 1880s he joined his father's practice, and was made a partner. He died on 13 August 1941 in the General Hospital, Altrincham, Cheshire.
The earlier works of the practice were in and around Bury, and consisted of small shops and schools, and larger churches and chapels. Their first major contract resulted from winning the competition in 1871 for the design of Cambridge Hall (1873–74) in Southport, Lancashire. This commission led to the firm being appointed as architects to the Southport Pavilion and Winters Garden Company, for whom they designed the Southport Winter Gardens (1874), the first such building for the seaside leisure market. James Maxwell became director of the St Annes on Sea Land and Building Company and the partnership became its architects and agents. They worked with the Clifton family of Lytham Hall in designing the layout of the resort, and in designing houses, hotels, and the promenade in 1874–77. The practice continued to undertake local commissions, and they also took part in competitions for larger works. In 1883 they won the competition for the design of the Ulster Reform Club in Belfast (1883–85), and came second in the competition for Belfast Central Library.