Roy originally trained in physics at Imperial College (BSC 1968, PhD 1971). He retrained in Medicine at the University College London graduating in 1979. He was appointed consultant oncologist in Glasgow in 1987, specialising in Neuro-Oncology and Head and Neck cancer. He was elected FRCP (Glas) in 1991 and FRCP (UK) 2004. He was promoted to full professor in 2000 and was head of the University department of Radiation Oncology at Glasgow University until 2010.
He has had extensive research interests into the treatment of brain tumours and was a member of numerous research boards in the UK and Europe. He has taught and examined extensively within the discipline of clinical oncology. He has been a long-term member of the Beatson Cancer Charity committee.
Since retirement he has been clinical lead for the Scottish Neuro-Oncology Network and chairs several committees on behalf of Cancer Research UK.