Wilkes was born at Dudley in Worcestershire, and educated at Cambridge University. After working on operational research during World War II, he returned to Cambridge where he was appointed professor of computing technology in 1965, a post he held until his retirement in 1980.

In 1946 Wilkes attended a course on the design of electronic computers at the Moore School of Electrical Engineering at the University of Pennsylvania. Here Wilkes learned of the direction modern computers would have to follow. Earlier models, such as the Moore School's ENIAC, were really designed to deal with one particular type of problem. To solve a different kind of problem thousands of switches would have to be reset and miles of cable rerouted. The future of computing lay with the idea of the ‘stored program’, as preached by John von Neumann at the Moore School.

Consequently Wilkes returned to Cambridge to begin work on EDSAC (Electronic Delay Storage Automatic Computer). In order to store a program, the computer must first have a memory, something lacking from ENIAC and earlier devices. Wilkes chose to adopt the mercury delay lines suggested by J. P. Eckert to serve as an internal memory store. In a delay tube an electrical signal is converted into a sound wave traveling through a long tube of mercury with a speed of 1450 meters per second. It can be reflected back and forth along the tube for as long as necessary. Thus assigning the number 1 to be represented by a pulse of 0.5 microsecond, and 0 by no pulse, a 1.45-meter-long tube could retain 1000 binary digits.

EDSAC came into operation in May 1949, gaining for Wilkes the honor of building the first working computer with a stored program; it remained in operation until 1958. The future, however, lay not in delay lines but in magnetic storage, and EDSAC soon became as obsolete as ENIAC.

Wilkes provided a lively account of his work in his Memoirs of a Computer Pioneer (1985).