His father, George Victor Murrell, was a salesman and bakery manager, and his mother was Winifred Edith née Walker.

He then started a Ph.D. in physics at KCL with Professor Christopher Longuet-Higgins, who soon afterward, was appointed to the Chair of Theoretical Chemistry at the University of Cambridge.

[2] In September 1957, he returned to Corpus Christi and branched out into applications of molecular orbital theory, collaborating variously with Edgar Heilbronner, visiting from Zürich, Alan R. Katritzky, and Norman Sheppard.

Murrell retired to become an emeritus professor in 1997; he "maintained an active interest in chemistry regularly working in the University and helping students until a few months before his death.

"[5] The John Murrell Fund was set up upon his death in 2016 to support Sussex Chemistry Ph.D. students facing financial difficulties.

In the 1960s, they had two sons and two daughters, all born in different places: Catharine (Cambridge), Luke (Sheffield), Ruth (Florida), and Adrian John (Sussex).