Charging overseas patients for NHS care in England must be suspended until it is clear it is not harming women, the Royal College of Midwives has said.
A couple whose baby died following an emergency Caesarean were not given the body as they were unable to pay £10,000 in medical fees, one doctor has said.
Joe Rylands said the expansion of charging had caused "disbelief" among many colleagues.
The Department of Health said the charges had raised £1.3bn since 2015.
In 2018, Dr Rylands was working in a maternity hospital when a woman from Western Europe on holiday in the UK came in - she was eight months pregnant and had started bleeding. Obstetricians performed an emergency Caesarean but the baby died.
When she and her partner were recovering on a ward, they were interviewed by an overseas visitors manager, in charge of billing.
Because they did not have a valid European Health Insurance Card (EHIC) they were told they had to pay £10,000 for the care they received - which they could not do.
"There's a service the NHS offers when you've had a miscarriage or when your baby has died - they can present it to you, the body in a bassinet, you take it home to have a funeral," Dr Rylands explains.
"That can be a really important process in grieving and recovery. And this couple were not allowed to have the body because they hadn't paid the [treatment] bill."
The hospital trust involved in the case declined to comment.
It was following the guidelines in billing the parents.
Since 2017, service providers have had a duty to check the eligibility of patients and charge them before non-urgent treatment in a bid to clamp down on so-called "health tourism". There are exceptions - such A&E - where treatment is free until a patient is either admitted to hospital or given an outpatient appointment.
Patients from inside the European Economic Area with a non-UK EHIC are treated for free, with the government applying to their home countries to cover the cost.
Those from elsewhere will be charged for the cost of their treatment.
There is growing opposition to the policy, with the British Medical Association calling for it to be abandoned completely.
The Royal Colleges of Physicians, Paediatrics and Child Health, Obstetricians and Gynaecologists and the Faculty of Public Health have written to ministers urging them to suspend the system.
The Royal College of Midwives told the BBC maternity care should be exempt from charges.
Sean O'Sullivan, head of health and social policy, said: "It could put off women who need care but are frightened that they may not be able to pay in the longer term. This is potentially dangerous for the woman and her developing baby."
Shadow home secretary Diane Abbott described upfront charging as "immoral" and said it should be suspended.
"Let's find out what the size of the problem is, but also we need to look at how people may be suffering."
The Department of Health has conducted a review of the 2017 amendments and said there was no significant evidence they have "led to overseas visitors being deterred from treatment".
This review has not been published.
England's Health Secretary Matthew Hancock told Victoria Derbyshire this was because of concerns over patient confidentiality.
He described the policy as a whole on charging overseas patients as "extremely reasonable" with "strong public support", but said that it needed to be implemented properly.
Mr Hancock said the rules were clear that maternity care should be free for couples who are not expecting to give birth in the UK. He added that he would look further into what happened with the couple who were unable to take their baby's body home,
"We must treat people with humanity and respect," he added.
One former NHS worker, who left his job in the overseas visitors department at a large London hospital last year, said he received no formal training in how to issue bills.
He said rules were not applied consistently - and "easy targets" were made of those less likely to "kick up a fuss".
"I think potentially at the moment the way it's being done is discriminatory," the man - who we are not naming - adds, targeting those with "foreign-sounding names" who were perceived to be less likely to be resident in the UK.
He described how he informed patients about fees when they had only just recently stabilised in intensive care.
Last December, Nasar Ullah Khan was receiving end-of-life care when he was handed a bill for £16,000 in his hospital bed.
He had suffered heart failure - but was ineligible for a transplant because he was not in the UK legally.
Mr Khan had tried and failed to legalise his status - and just before he fell ill, had applied to the Home Office for voluntary return to Pakistan.
He died in February.
Liz Bates, a Birmingham GP who volunteers at the charity Doctors of the World, was contacted to help the family and says: "Almost as soon as they knew Nasar wasn't eligible for free NHS care they started talking to him about billing."
The family were posted another bill for £32,000, and another for £23,000, which Ms Bates said had caused them deep stress and was "totally unnecessary" because Mr Khan would never be able to pay the bills.
A spokesman for University Hospitals Birmingham NHS Foundation Trust said it was obliged by law to implement the charging regulations.
"Further guidance published by the Department for Health and Social Care also states that patients must be fully informed about the charges they might face, therefore one initial invoice was provided to Mr Khan, with two further invoices issued to a home address."
A Department of Health spokesman said: "British taxpayers support the NHS so it is only right that overseas visitors also make a contribution to our health service so everyone can receive urgent care when they need it and, since 2015, charges for people who are not UK residents have secured an extra £1.3bn for front-line NHS services.
"Importantly, our guidance is clear that urgent treatment must never be withheld, if someone cannot pay."
But campaigners against the charges argue that, in practice, decisions about urgency are not clear cut. James Skinner, from campaign group Medact, says many healthcare workers do not know the guidelines.
"Doctors are not well trained to assess a person's immigration status, and overseas managers are not trained to make clinical judgements - we regularly see people with cancer who are denied treatment."