Oswald Archer was born in Armley, near Leeds, Yorkshire, England on 24 October 1871. In the England census of 1901 his occupation is given as Architect's Assistant and in the 1911 England census it is given as Architect and Surveyor, however it is not known where or with whom he trained as an architect. He had evidently begun practising as an independent architect about 1905. In 1906 he was appointed architect to the Salvation, a position he held until 1936.
On 6 May 1915 Archer was made a Freeman of the City of London
10 Victoria Street, London in 1910; Westwood, Essex Road, Leyton, Essex in 1911 and 1915; and 5 Blackthorne Drive, Chingford, Essex in 1939
In the 1939 England and Wales Register Archer gave as his occupation retired architect.
Among the many buildings Archer designed for the Salvation Army were the Salvation Army Hall in Constitution Street, Dublin in (1908-09); Salvation Army Hall, Wolverhampton (1910); Salvation Army Hall in North Street, Portslade (1910; Salvation Army citadel, Victoria Street, St Albans (1911); Salvation Army Hall in York Road, Belfast (1911); Salvation Army Citadel, Worthing, Sussex (1912); the headquarters of the Salvation Army in Dublin (1912-13); and Salvation Army William Booth Memorial Halls in Nottingham (1914-15); an addition to the Salvation Army Hall in York Road, Belfast (1926-27); Salvation Army Hall, Bradninch, Devon (1930); Men's Hostel for the Salvation Army, Bute Street, Cardiff (1934)