Reginald Annandale Cordingley was born in Sale, Cheshire, England on 12 March 1896 and was articled to Robert John McBeath (1865-1932) in 1911. He also attended evening classes at Manchester Technical College. His training was interrupted by the outbreak of World War One in which he served in the Army for four years. After the war he resumed his studies and in 1919 entered the School of Architecture, University of Manchester where he received several awards including the Henry Jervis Travelling Scholarship in 1920 and 1921 and the Manchester Institute of Builders Travelling Scholarship in 1922. In 1923 he was awarded the Rome Scholarship in Architecture and from 1923 to 1926 attended the British School in Rome.
Following his return to England he took up a teaching post at Durham University. He was also appointed resident architect of Durham Cathedral and in 1929 Master of Architecture at Armstrong College, Durham University, and subsequently Director, of the School of Architecture and Town Planning, a post he held until 1933.
In 1933 succeeded Archibald Campbell Dickie (1868-1941) to the Chair of Architecture at the School of Architecture, Manchester University.
In 1926 he formed the architectural partnership Cordingley & McIntyre with Donald McIntyre. The practice had offices in Durham and Manchester. They designed several churches, mainly in the north-east of England. They also designed the Central Library in Chelmsford, Essex (1935); eight houses in Wilmslow, Cheshire (1936); gas showrooms in Durham (1940); Durham Johnston School in Durham (1952); and Maiden Castle Sports Hall, Durham University (1962-65). The eight houses they designed in Sale are discussed in Small Houses £500-£2500, edited by H. Myles Wright (1937 pp. 82-84). The practice was dissolved in 1969.
Cordingley died in Manchester on 28 November 1962