Ministers face renewed claims that GP surgeries are being turned into border posts today, as the coalition unveils details of its plans to charge overseas visitors £200 to use the NHS.
The annual charge, which would apply to anyone wanting to use the NHS who is staying in the UK for longer than six months, would prevent visitors from receiving the full access to primary care and accident and emergency they enjoy at present.
It is not clear what proportion of overseas visitors travel to Britain with the primary goal of taking advantage of the free care offered by the NHS.
But Hunt, who is publishing a consultation on the issue today, argued that the NHS fails to collect £12 million from people who should be paying for their treatment but do not.
"That alone is 2,000 hip operations, which is significant," he told the Today programme.
"We will be very careful because we want to get this right, but one of the big questions in the spending review was the sustainability of the NHS going forward.
"Is it sensible it is so easy for anyone from overseas coming to the UK to get an NHS number that means they have a passport for the whole system?
"Sorting out this problem is something we really have to do for the long term."
Part of the solution could be changing the incentives system, by getting hospitals to claim the money centrally rather than having to follow up the international paperwork.
Exemptions would apply for public health concerns relating to TB, Hunt said. He insisted other countries were able to run charging systems while protecting against public health issues, but Labour voiced broader doubts about the implementation of the changes.
"In its three years in power the government has a poor record on announcing policies that sound good but prove to be completely unworkable," shadow health minister Liz Kendall said.
"We will have many questions to ask about the details when they are published but the key tests for their proposals are: can they be properly enforced and will they save more money than they cost to put in place?
"The public and NHS staff must be confident that any new measures are about getting taxpayers a better deal and ensuring fairness, not playing politics with our NHS."
Today's moves were originally announced in the Queen's Speech, when the government announced measures in the immigration bill which would force temporary migrants to "make a contribution".
The proposals prompted howls of protest from the Royal College of General Practitioners. Its chair Dr Clare Gerada warned that "GPs must not be a new 'border agency' in policing access to the NHS".
"While the health system must not be abused and we must bring an end to health tourism, it is important that we do not overestimate the problem and that GPs are not placed in the invidious position of being the new border agency," she said.
Some have criticised ministers for rushing through the proposals with a rapid consultation which ends in August. But David Cameron first raised the issue back in March, when he said the 'something for nothing' culture would be attacked in public services.
"What we have is a free national health service, not a free international health service," the prime minister said.
"So, let me put it very simply: we're going to get much better at proper reciprocal charging. Wherever we can claim back the cost of NHS care, we will. If someone visiting the UK from another EEA country uses our NHS, then it is right that they or their government pay for it.
"British taxpayers should support British families and those who contribute to our economy. And for migrants from outside the EEA, we want to introduce stricter charging or a requirement for private health insurance to cover the costs of NHS care."