Ipgrave was born on 19 April 1958 in Northampton, Northamptonshire, United Kingdom. He was educated at Magdalen College School, Brackley, a state school in South Northamptonshire. From 1975 to 1978, he studied mathematics at Oriel College, Oxford, and graduated from the University of Oxford with a first class Bachelor of Arts (BA) degree. From 1979 to 1982, he trained for ordination at Ripon College Cuddesdon, an Anglican theological college near Oxford. During that period he also studied theology at the University of Oxford, and graduated with an additional first class BA. In 1999 Ipgrave completed a doctorate at Durham University with a thesis entitled Trinity and inter-faith dialogue: plenitude and plurality.
Ipgrave was ordained in the Church of England: made a deacon at Petertide 1982 (27 June) and ordained a priest in the Petertide following (26 June 1983) — both times by Douglas Feaver, Bishop of Peterborough, at Peterborough Cathedral. After a curacy in Oakham followed by time in Japan, he was a team vicar in two separate Leicester parishes.
In Leicester, in 1991, he was appointed diocesan chaplain for relations with people of other faiths, and bishops' domestic chaplain in 1992. He was appointed Archdeacon of Southwark in 2004. In 2010 he also became Canon Missioner of Southwark Cathedral. He was co-chair of Southwark and London Housing Association (now Amicus Horizon)
He was formerly Inter Faith Relations Advisor to the Archbishops' Council and secretary of the Churches' Commission on Inter-Faith Relations.
On 3 February 2012, Ipgrave was announced as the next Bishop of Woolwich, an area bishop in the Diocese of Southwark. On 21 March 2012, he was consecrated a bishop, by Rowan Williams, Archbishop of Canterbury, during a service in Southwark Cathedral. He also served as Warden of Readers for the diocese. In May 2013, he read bidding prayers at a Mass for Lee Rigby who was murdered by Islamists in the 2013 Woolwich attack.