Woodall has a BA degree in history from the University of York and an MA and PhD from the Courtauld Institute.
Woodall was a Speelman Fellow in Dutch and Flemish Art at Wolfson College, Cambridge, from 1980 to 1982,[1] and an assistant curator at Christ Church Picture Gallery, Oxford, from 1982 to 1985.
[2] She spent a year on a Leverhulme Fellowship at the University of Leiden.
Woodall has also been a member of the editorial board of the Nederlands Kunsthistorisch Jaarboek (Netherlands Yearbook for History of Art) (until 2023).
[3] In 2010, Woodall was with a group of Courtauld students protesting about increased university tuition fees when they reportedly received rough treatment from the Metropolitan Police with Woodall herself being picked up by an officer and thrown into a group of protestors.