Bullard was born in Norwich and educated at Cambridge University. After war service in naval research he returned to Cambridge as a reader in geophysics before accepting a post as head of the physics department of the University of Toronto (1948) and visiting the Scripps Institute of Oceanography, California, (1949). After a five-year spell as director of the National Physical Laboratory, he returned to Cambridge as a reader and later, in 1964, professor of geophysics and director of the department of geodesy and geophysics. Here he remained until his retirement in 1974.

Bullard made a number of contributions to the revolution in the Earth sciences that took place in the 1950s and 1960s. He carried out major work on the measurement of the heat flow from the Earth. It had been assumed that as the ocean floor was less rich in radioactive material than the continental crust, it would be measurably cooler. The technical difficulties of actually measuring the temperature of the ocean floor were not overcome until 1950, and in 1954 Bullard was able to announce that there was no significant temperature difference between the continental crust and the ocean floor. This led Bullard to reintroduce the idea of convection currents.

In 1965 Bullard studied continental drift, using a computer to analyze the fit between the Atlantic continents. An excellent fit was found for the South Atlantic at the 500-fathom contour line. However, a reasonable fit could only be made for the North Atlantic if a number of assumptions, such as deformation and sedimentation since the continents drifted apart, were taken into account. Later, when independent evidence for these assumptions was obtained, it gave powerful support for the theory of continental drift.

Bullard was knighted in 1953.