He was Reader in functional analysis and Vice-Master of Churchill College at Cambridge University.
[1] After serving in the Royal Air Force from 1955 to 1957, he entered Sidney Sussex College, Cambridge, and continued at Cambridge for his graduate studies, receiving a PhD in 1964 under the supervision of Frank Smithies.
[1][4] Back at Cambridge, he was promoted to Reader in 1980 and was Vice-Master of Churchill College from 1990 to 1993.
[1] In 1969, Allan won the Junior Berwick Prize of the London Mathematical Society.
[5][6] He contributed to section III.86 in the book The Princeton Companion to Mathematics edited by Timothy Gowers, but did not live to see his article "The Spectrum" in print form published in 2008.