After serving as a Pilot Officer in the Royal Air Force, Strudwick entered Kelham Theological College (1952), which was run by the Society of the Sacred Mission.
He was Ecumenical Planning Officer for Education for Milton Keynes 1977–80, living in association with the Society of the Sacred Mission at Willen with his wife and three children.
In 1994 he became a Fellow and Tutor of Kellogg College, Oxford, and a member of the Theology Faculty, being granted the status of a Master of Arts in the university.
He was Associate Chaplain of Corpus Christi College, Oxford, from 1999 to 2007 and taught on numerous out-of-term programmes such as the Smithsonian and continued with tutorial work for the Faculty of Theology as an Emeritus member.
Strudwick has been an Honorary Canon of Christ Church, Oxford since 1982 and on 21 July 2009 he was awarded the Lambeth Degree of Doctor of Divinity by the Archbishop of Canterbury for his "outstanding work in theological and ministerial education and as an historian for his research on the English Reformation and Richard Hooker".