William Bailey Wheatley was born in Hull, Yorkshire, England on 6 July 1887. It is not known where or with whom he trained as an architect. In 1907 he formed a partnership, Blanchard, Wheatley & Houldsworth. in Hull with William Boyer Blanchard (1886-1959) and Austin Frank Houldsworth (1883-1933). The partnership was dissolved in 1924 and Wheatley and Holdsworth established their own practice, Wheatley & Houldsworth which was active in Hull until at least the 1950s.
Wheatley was elected a Licentiate of the Royal Institute of British Architects (LRIBA) in 1925 and a Fellow of the Royal Institute of British Architects (FRIBA) in 1938.
His address was given as 20, Saville Street, Hull in 1923; Bridge Chambers, Monument Bridge, Hull. in 1926; Savile House, Savile Street, Hull 1939; and 236 Victoria Avenue, Kingston-upon-Hull in 1961. He died at 135 Princess Avenue, Kingston-upon-Thames on 20 November 1961