The British government says visitors could be required to hold health insurance before they can enter the country.
The BBC says the move is an attempt to crack down on "health tourists" who come for treatment but fail to pay for it.
In a separate immigration review, Britain could also refuse entry to foreigners owing money for health care. Ministers say this would stop people from overseas taking advantage.
Britain's National Health Service (NHS) is paid more than $NZ50 million a year by overseas visitors, but writes off another $NZ10 million in unpaid bills.
If the proposals are approved, migrants with unpaid bills will be turned away by the UK Border Agency if they try to re-enter the country without settling their debts.
The proposals would not cover visitors from the European Economic Area and other countries with whom Britain has reciprocal health agreements.