Noreen Murray is Professor Emeritus in the Institute of Cell and Molecular Biology of the University of Edinburgh, the same department as Anthony Trewavas. She is a Fellow of the Royal Society and served as a member of the Society's Council as well as on the Council of the Biotechnology and Biological Sciences Research Council.

Murray was chair of the Royal Society group that set the remit for the peer review of Dr Arapad Pusztai's work. The group returned a critical report  even though they did not have Pusztai's full data but only a report meant for internal use among Pusztai’s colleagues. She had earlier sat with Derek Burke on the Royal Society's working group on 'Genetically Modified Plants for Food Use'. In other words, her views on the GM issue were already established.

With her husband, Professor Sir Kenneth Murray (co-founder of the first European based biotech company, Biogen) and Professor Jean Beggs, Prof Noreen Murray invented the first genetically engineered vaccine (for Hepatitis B, engineered into yeast) that was approved for human use. With financial support from the pharmaceutical industry-funded Wellcome Trust, Noreen and Kenneth Murray founded the Darwin Trust in Edinburgh, which conducts biotech research.