Christians in the House of Lords have supported a number of amendments to the government's Illegal Migration Bill.
Peers voted in favour of amendments providing safeguards for unaccompanied child migrants and victims of modern day slavery.
Speaking during the debate, the Bishop of Chelmsford, the Rt Rev Dr Guli Francis-Dehqani, said it would be "unforgivable" to allow unaccompanied child migrants to "languish in perpetual limbo".
"This Bill will prevent potentially thousands of children from ever claiming refugee protection in the UK however serious their protection needs may be and disturbingly, regardless of the fact that they may not have had any say in the decision to travel here irregularly," she said.
"Let's be absolutely clear, this means vulnerable unaccompanied children who have fled unimaginable horrors will arrive to find they will be detained and then potentially accommodated by the Home Office outside the established care system. And this is all, not in order for their asylum case to be heard and assessed, but simply to deter others.
"Given that there are no return agreements yet in place and the Government has not provided any new information as to how returns will exponentially increase, the overwhelming majority of individuals will be left to languish in perpetual legal limbo and financial precarity.
"I would argue this is unacceptable for any asylum seeker but for an unaccompanied child, it is unforgivable."
The amendments also had the support of the Bishop of Durham.
The Bill was introduced by the government earlier this year to prevent small boats crossing the English Channel.
It has come under fire over plans to send people arriving illegally in the UK to Rwanda or other "safe" third countries. The Supreme Court yesterday ruled these plans unlawful.
The amendments made by the House of Lords will be considered by MPs at a later stage.
Catholic international development agency Cafod has said the Illegal Migration Bill "represents everything Pope Francis asks us not to be".
It is asking its supporters to write to their MPs urging them to vote against the Bill.
Aisha Dodwell, head of campaigns at Cafod, told the PA news agency: "If passed, this inhumane legislation will be a stain on the country's reputation.
"People fleeing conflict and persecution are dying in their thousands as they try to find safety for themselves and their families.
"Yet, instead of recognising the dire situation these people are in, the UK Government is seemingly doing everything it can to make their lives even harder.
"Pope Francis has urged world leaders to build bridges not walls and to welcome, protect and integrate people without distinction.
"But the Illegal Migration Bill represents everything Pope Francis asks us not to be, which is why we are urging Catholics to speak out against the Bill and show we are a country that welcomes people who need our help."
