Glennie worked with Alan Turing on several projects, including the Manchester Mark 1. He also played the first ever game of computer chess, although it was played against a program not capable of being run on the computers of the day: the chess program was devised by Alan Turing, and operated with pen and paper by Turing. The match took several weeks to complete and Glennie came out the victor.
Glennie subsequently worked at Atomic Weapons Research Establishment (AWRE) where he was responsible in the early 1960s in developing FORTRAN compilers for several large computers inc. IBM 709, IBM 7090, IBM 7030 ("Stretch") and also ICT Atlas. He pioneered a method of developing the compiler for the Atlas on the IBM 7030 in advance of delivery of the Atlas, using an interpretive technique.