In a letter to The Times, Bishop Paul, who leads on refugee issues for the Church of England in the Lords, argues that the needs of those fleeing war and persecution should not be "crowded out" from debate about the UK's future place in the world.
Instead, discussions about Brexit could offer an opportunity to find ways to make Britain a more "welcoming and compassionate place", the letter argues.
The letter is co-signed by the Bishop of Croydon, Jonathan Clark, Chair of Churches' Refugee Network, and Commissioner Clive Adams, Territorial Commander for The Salvation Army in the UK and Ireland.
They offer support to cross-party calls for the appointment of a Minister for Refugees and an extension to the transition period for asylum seekers given refugee status from 28 days to 50.
The letter also urges voters to press candidates of all parties to commit to working both locally and nationally in support of the Community Sponsorship scheme.
"The refugee camps across the world were there before the election was called and they will be there after 8th June," the letter notes.
"A new parliament cannot be allowed to move on from the refugee crisis.
"Rather than crowding out our response to the global refugee crisis, discussions around Brexit should compel us to ensure that a post-Brexit Britain will be a welcoming and compassionate place."
Notes to editors:
The full text of the letter is here
The Bishop of Durham was a member of the panel set up by the All Party Parliamentary Group on Refugees to investigate the experience of new refugees in the UK.
The panel's report, "Refugees Welcome?", is available here
The Community Sponsorship Scheme was launched at Lambeth palace in July 2016. More details here