Piecing together multiple Google snippets from The University of Leeds Review, Vol. 38, 1995, p. 249:
Alan Earnshaw retired from the School of Chemistry in September 1995. After graduating from Sheffield in 1955 , he obtained the degree of PhD at London in 1958, and then served as a lecturer at Battersea College of Technology until his arrival in Leeds as a lecturer in the Department of Inorganic and Structural Chemistry at a salary on the scale £1,000 ...
The German Wikipedia provides some additional details: Earnshaw received a bachelor degree at Sheffield, and his employment at the University of Leeds commenced in 1966. Earnshaw is the author of three books:
Alan Earnshaw, Introduction to Magnetochemistry. London: Academic Press 1968. 115 pp.
A. Earnshaw and T.J. Harrington, The Chemistry of the Transition Elements. Oxford: Oxford University Press 1973. 101 pp.
N.N. Greenwood and A. Earnshaw, Chemistry of the Elements. Oxford: Pergamon Press 1984. 1542 pp.
While I was able to find UK obituaries for people with the name Alan Earnshaw, none of them appear to be for the professor of chemistry. Based on the date of retirement and the year he received his bachelor degree, Earnshaw was likely born around 1930. Publicly available UK birth records show several potential candidates, but without a known place of birth it is impossible to identify any of those as the relevant one.