[7] He studied at the Simon of Cyrene Theological Institute, then at Oak Hill College in London, receiving a Bachelor of Arts degree in 1994.
[1][4] Wambunya took orders in the Church of England: he was made deacon at Petertide 1997 (28 June) by Richard Chartres, Bishop of London, at St Paul's Cathedral;[8] and ordained priest the following Petertide (4 July 1998) by Graham Dow, Bishop of Willesden, at St Martin's Church, Ruislip.
[1][4] Wambunya was consecrated as the third Bishop of Butere on 6 October 2013,[10] succeeding Horace Etemesi (1993–2003) and Michael Joshua Sande (2003–2013).
[11][12] As Bishop of Butere he attended and led a seminar at the 2018 Global Anglican Future Conference, but he would later criticise the movement, saying in 2020 "Personally, I think the Gafcon axis has become obsessed with the matter of sexuality.
[5] In September 2024, Wambunya was formally rebuked by the Church of England after ordaining Revd Wamare Juma of the Revealed Evangelical Mission, a "non-denominational para-church" not in communion with the Church of England, as a bishop in a service in Germany in April of that year.