On 8 May 2001, Conry was appointed the fourth Bishop of Arundel and Brighton by Pope John Paul II.

On 27 September 2014, Conry announced his resignation as Bishop of Arundel and Brighton with immediate effect for having "been unfaithful to [his] promises as a Catholic priest" and bringing "shame" on the diocese and the Church.

[8] In an interview with The Catholic Herald newspaper published in December 2008, he was reported to have said that it does not make much sense to talk about salvation to young people "unless you speak in their own language.

"[9] He has criticised society's "moral confusion": "we preach a liberal attitude to relationships and allow the media and commercial interests to prey on our young people, so that they are turned into little adults long before their time.

Then we shake our heads in dismay and shame when we learn that we have the highest teenage pregnancy in the EU, six times higher than Holland.

[9] In a May 2009 pastoral letter, he urged a more adult approach to the sacrament of reconciliation: "Go to the priest and talk about these things, the way in which your relationship with God might have grown stale.

[11] He is reported to have stated that Summorum Pontificum does not suggest significant change because the Tridentine Mass caters for a small group of people.