He received the American Nuclear Society's 2023 Edward Teller Medal Award "for pioneering research in the use of high-intensity lasers for producing unique electron, ion, and x-ray beams for scientific applications in fast ignition fusion, advanced accelerators and probing of plasmas". Before then, he was awarded the 2013 Institute of Physics' Payne-Gaposchkin Medal and Prize for his original contributions to relativistic laser-plasma interaction physics, the 2006 American Physical Society’s Award for Excellence in Plasma Physics Research for his contributions to inertial fusion science and, as UK team leader, the 2007 Daiwa Adrian Prize for UK-Japan collaborative investigations into new areas of high energy density science. He is currently William Penney Fellow of AWE, a Fellow of the Institute of Physics and of the American Physical Society. He is a visiting Professor to Imperial College London and Shanghai Jiao Tong University. He was Individual Merit Fellow of the Rutherford Appleton Laboratory and member of the Science and Technology Facilities Council's Senior Leader Team between 2007-2021.

Peter Norreys chairs the Department of Physics' Awards Committee, is Director of Graduate Studies in Atomic and Laser Physics, and serves as one of the elected members of the Physics Management Committee. He is currently co-ordinator of the Oxford-Imperial-Warwick "Centre for Postgraduate Training in Plasma Physics and High Energy Density Science" graduate course. Peter Norreys is Supernumerary Fellow to University College where he is Dean of Degrees.