After attending Central Newcastle High School she matriculated at Westfield College at the University of London, where in 1964 she received a Bachelor of Arts with first class honours.
[1][4] During her time at the British Museum, Webster was the co-curator for four major exhibitions about the Early Middle Ages.
[5] Webster has served since 2002 as an honorary visiting professor at the Institute of Archaeology at University College London, and on the advisory panel of the National Heritage Memorial Fund since 2012.
[1][5] She has also served as a trustee for the Society of Antiquaries of London,[5][4][7] an organisation of which she was elected a fellow in 1973,[1] in addition to memberships on the English Heritage Museums and Archives Advisory Panel, and the British Academy Corpus of Anglo-Saxon Stone Sculpture Committee.
[5] From 1986 to 1999 she served as the UK representative for the Koordinierend Ausschuss der Internationalen Arbeitsgemeinschaft für Sachsenforschung.