Health secretary Jeremy Hunt will ask GPs to crack down on the use of free NHS services by non-Britons, under controversial plans to be unveiled this week. A registration and tracking system, possibly linked to NHS numbers, will allow practices to spot people who do not qualify for free healthcare.

It is one of several measures to be announced by Hunt that are designed to close so-called "NHS tourism" loopholes that allow non-eligible immigrants access to care without being identified or charged. These will not restrict access to emergency treatment, but some people will be required to pay for anything else. It is understood the plans will be developed, working with GPs, to ensure that people can use services when they really need to.

The government is keen to address concerns that such proposals could force doctors to break their Hippocratic oath to act in the best interests of their patients. Some critics claim the coalition is unfairly targeting immigrants in response to the success of Ukip in recent local elections.

The cost of immigrants' illegitimate use of health services is estimated to be £33m, a fraction of the NHS's £109bn annual budget. The plans will be unveiled this week before a cross-government agenda that aims to crack down on non-Britons' abuse of government services. Proposals include tightening up systems for claiming back costs from EU visitors' home countries when they use the NHS: the coalition believes the system fails to identify thousands of Europeans every year, effectively giving them free healthcare.

The changes will also protect UK expatriates by giving them access to free NHS healthcare for life once they have paid national insurance contributions for 10 years. At present, anyone living permanently outside the UK faces paying for NHS care they receive.

Hunt has also ordered an audit of the true cost of use of the NHS by foreign nationals. He told the Observer: "No one expects health workers to become immigration guards, and we want to work alongside doctors to bring about improvements, but I'm clear we must … protect the NHS from costly abuse.

"We want a system that is fair for the British taxpayer by ensuring foreign nationals pay for NHS treatment. By looking at the scale of the problem and at where improvements can be made, we will help ensure the NHS remains sustainable for many years to come."

The NHS treats 1m people every 36 hours, but the current system does not capture every chargeable visitor. In 2011-12, the NHS identified that foreign nationals should have paid £33m. A Department of Health analysis suggests that fewer than half of overseas visitors using hospitals are identified and only half their costs recovered. Some unofficial reports have speculated the cost is higher – in 2003, CCI insurers estimated it at £50m-£200m.

The proposals follow a government review which found that some people visiting the UK for a short time are unfairly receiving healthcare, largely because the UK's rules are more generous than those of most other countries.