Patients may be required to show their passports at hospitals under new Government guidelines to tackle health tourism.
New charges were introduced last week for overseas visitors and migrants who use NHS hospital services in England.
The Department of Health (DoH) said these plans will help recoup up to £500 million a year by 2017/18.
All patients will be asked questions about their residence status in the UK whenever accessing a new course of treatment, a spokeswoman said.
If there is uncertainty about their residence status, they may be required to submit documentation, including passports and immigration documents.
But no one will be denied urgent treatment while charges are being determined.
Treatment in A&E departments and at GP surgeries will remain free for all.
Anyone from outside the European Economic Area (EEA) coming to the UK for longer than six months is now required to pay a "health surcharge" as part of their visa application.
The £200-a-year fee is reduced to £150 for students.
"The surcharge will ensure that those coming to work, study and join family in the UK make an appropriate financial contribution to the cost of the health services they may use whilst in the UK," the DoH said.
A study estimated that £388 million is spent each year on patients who find themselves in need of health care while in England and who should already be paying for their care, but who are often not processed and charged by the NHS. Only around 16% was being recovered.
The spokeswoman said hospitals will receive an extra 25% on top of the cost of every procedure they perform for an EEA migrant or visitor with a European Health Insurance Card (EHIC).
Short-term visitors from outside Europe will be charged 150% of the cost of treatment.
The DoH also previously said it is looking at piloting ways the NHS could recover costs from international visitors seeing GPs.
On Friday, Mr Hunt told Radio 5 Live that the Government needed to get better at charging people from abroad for using NHS services, citing France, Germany and Spain as being far more efficient at claiming costs back.
"If you're not paying for the NHS through your taxes, then you should be charged for your use of the NHS," he told the studio audience.
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