Willmott undertook an undergraduate degree at St Peter's College, Oxford before training for the ministry at Westcott House, Cambridge. He was a curate at St George's in Norton in the Diocese of St Alban's between 1974 and 1977.
From 1978 to 1979 he was Assistant Chaplain of Oslo with Trondheim before moving to become Chaplain of Naples with Capri, Bari and Sorrento between 1979 and 1983. He was also Officiating Chaplain to HM and American Forces in Southern Europe between 1979 and 1983. All of these appointments were in the Diocese of Europe.
In 1983, Willmott returned to the UK as Rector of Ecton and Warden of the Peterborough Diocesan Retreat House at Launde Abbey. In addition to these posts, he became Diocesan Director of Ordinands and of Post-ordination Training in 1986; continuing with his director roles having relinquished his posts of Rector and Warden in 1989.
Willmott was made Canon Residentiary and Precentor of Peterborough Cathedral in 1989; holding these posts and continuing with his director roles until 1997, when he became Canon Residentiary of Durham Cathedral and Archdeacon of Durham. He relinquished these posts in 2002 following his ascension to the episcopate. Willmott replaced the Rt. Revd. Geoffrey Rowell following Dr Rowell's appointment as Bishop of Gibraltar.