Webb was born in 1937 and educated at the University of Nottingham and Oriel College, Oxford. After working in laboratories in Murray Hill, New Jersey, Webb returned to Oxford as a research fellow in physics at the Clarendon Laboratory in 1968, and was appointed to a university lectureship in 1971, becoming Reader in 1990 and Professor in 1992. He was made a Fellow of the Royal Society in 1991. He served as Head of Atomic and Laser Physics from 1995 to 1999, and became an Emeritus Professor in 2002. Jesus College, Oxford appointed him to a Fellowship in 1973; he became a Senior Research Fellow in 1988 and an Emeritus Fellow in 2005. In 1977, he founded Oxford Lasers. He was made a Member of the Order of the British Empire in 2000. He was awarded the Duddell Medal and Prize in 1985 by the Institute of Physics and delivered the Paterson Lecture of the Royal Society in 1999. He is also a Fellow of the Optical Society of America.
His publications include (as editor in chief) Handbook of Laser Technology and Applications (2003) as well as various papers on lasers and laser mechanisms in academic journals and specialized books. He has also co-authored a textbook in laser physics in 2010, with Simon Hooker of Oxford.
Webb is considered a pioneer in British laser research and has made significant contributions in the areas of hollow cathode metal-vapor lasers, copper vapor lasers, copper vapor laser-pumped dye lasers, and excimer lasers.
- "Webb, Prof Colin Edward". Who's Who 2009. Oxford University Press. December 2008. Retrieved 7 March 2009.
- C. E. Webb, High-power dye lasers pumped by copper vapor lasers, in High Power Dye Lasers, F. J. Duarte (Ed.) (Springer, Berlin, 1991) Chapter 5. 
- S. Hooker and C. E. Webb, Laser Physics, (Oxford University Press, 2010) 
- J. A. Piper, G. J. Collins, and C. E. Webb, CW laser oscillation in singly ionized iodine, Appl. Phys. Lett. 21, 203-205 (1972).
- P. Gill and C. E. Webb, Electron energy distributions in the negative glow and their relevance to hollow cathode lasers, J. Phys. D: Appl. Phys. 10, 299-301 (1977).
- R. G. Caro, M. C. Gower, and C. E. Webb, A simple tunable KrF laser system with narrow bandwidth and diffraction-limited divergence, J. Phys. D: Appl. Phys. 15, 767-773 (1982).