After graduating Richards stayed at the University as a Fellow in Chemistry at Lincoln College from 1947–64. In 1964 he succeeded Sir Cyril Hinshelwood as Dr Lee's Professor of Chemistry at Exeter College. In 1969, he became Warden of Merton College. Richards held the post of Vice Chancellor of the University from 1977–81 and was Director of IBM (UK) Ltd from 1978–83 and Director of the Leverhulme Trust from 1984–93. He was President of the Royal Society of Chemistry for two years, and the Royal Society awarded him the Davy Medal in 1976 and the Royal Medal in 1986. He was knighted in 1977. He was also Chancellor of the University of Exeter from 1982 to October 1998. A painted portrait of Sir Rex Richards by Allan Ramsay hangs in the Senate and Council Chamber, Northcote House, University of Exeter, and another by Bryan Organ in Merton College, Oxford.