Webb has been awarded the EFOMP Medal by the European Federation of Organisations for Medical Physics, the Barclay Medal by the British Institute of Radiology, an Honorary Fellowship of the Institute of Physics and Engineering in Medicine, and honorary membership in the Deutsche Gesellschaft für Medizinische Physik e.V., the German Society for Medical Physics. In addition, he was awarded the degree of DSc (Med) Honoris Causa by the University of London.