Wilcockson attended Chigwell School and Merton College Oxford before taking on a number of teaching roles, including at Campbell College, Belfast and as Head of English and Deputy Headmaster at The Leys School, Cambridge. In 1973 he was elected a Fellow of Pembroke College and was Director of Studies in English and in Anglo-Saxon, Norse & Celtic as well as Tutor for Admissions and Assistant Tutor. He took up a lectureship in the Department of Welsh Literature at the University of Cardiff in September 1998. In 2018 he won the University of Cambridge's Seatonian Prize for the best English poem on a sacred subject, his fourth win, having also won the prize in 1995, 2009 and 2016. He was an Emeritus Fellow of Pembroke College. He died in March 2023.