Bishop Paul McAleenan warned the charges will prevent vulnerable people from receiving medical treatment and have been introduced without sufficient impact assessments.
Jonathan Cox, deputy director of Christian social justice charity Citizens UK, echoed Bishop McAleenan's concerns.
Speaking during News Hour Cox said: "People who need treatment are going to be less ready to actually look for that treatment and we know that might have a big effect in terms of infectious diseases.
"We know it will have a big impact in terms of people with developmental diseases that will not seek treatment until it's often too late."
The House of Lords will debate the changes on Thursday.
Speaking ahead of the debate, Bishop McAleenan said in a statement: "The level of concern expressed by medical professionals and charities, including several Catholic organisations, reflects how catastrophic the consequences of these new regulations are likely to be."
Migrants and visitors to the UK not eligible for free healthcare will from now on be charged upfront for the cost of their treatment, as rules come into force that also extend charging community health services and charities that receive NHS funding.
Cox told Premier why Christians should also be concerned about the charges.
He said: "The core principle of the NHS is that we must first do no harm and I think the problem with these charges is that it really violates that principle.
"As Christians, whether they are foreign or whether they are native-born or become citizens, we should care about that, we should want to make sure that people are able to live healthy and flourishing lives."
NHS trusts have been instructed to ask patients for detailed evidence to establish their right to free healthcare, if there is any doubt about their entitlement.
Every NHS trust has been issued with guidance, with a list of questions to be asked, and documents to be required, if the residence status of a patient is not immediately clear.
A small number of hospitals have introduced upfront charges for overseas patients already but the vast majority continue to chase debts after patients have left the hospital.
Listen to Jonathan Cox speaking with Premier's Tola Mbakwe:
