The European Commission is launching legal action against Spain over the refusal of some hospitals to recognise the European Health Insurance Card.
The EHIC entitles EU citizens to free healthcare in public hospitals.
But some Spanish hospitals rejected the card and told tourists to reclaim the cost of treatment via their travel insurance, the Commission says.
A BBC correspondent says the Commission is not accusing cash-strapped Spanish hospitals of trying to make money.
The Commission, which checks compliance with EU law, has requested information on the issue from the Spanish government - the first stage of an infringement procedure which could eventually result in a fine.
Under the health card system, an EU citizen's home health service is supposed to cover the cost of emergency treatment abroad. So for a British citizen the UK National Health Service picks up the final bill.
The EHIC is mainly intended for emergency treatment abroad, but also covers patients for pre-existing medical conditions. In cases where doctors think a European visitor's treatment can wait until they get home, then the EHIC can be deemed invalid.
The BBC's Matthew Price in Brussels says the EHIC is intended to give foreign visitors the same level of care in emergency cases as locals get.
But a British holidaymaker in Spain told him that when he went to hospital severely dehydrated he was told to give them his travel insurance details.
"When we were refused they were quick to ask for a credit card and then, at a later stage, insurance details. And when we tried to re-present the [EHIC] card to them, saying look this should work, they just dismissed it," holidaymaker Ray Burton said.
The Commission says it has had hundreds of such complaints concerning Spain. It says the much higher cost of private treatment is being passed on to the travel insurance companies "or, increasingly, is being billed to the citizens directly".
Among the complaints were ones from the UK Foreign Office and insurance companies in several European countries.
The BBC's Duncan Crawford says the British cases included a young boy with facial injuries who was turned away from a clinic despite showing his EHIC.
In another case, a British holidaymaker was treated in hospital for a month and a debt collection agency working for a Spanish hospital asked his travel insurance to pay £54,000 - even though the cost was covered under the EHIC scheme.
When asked about the dispute with the Commission, the Spanish health ministry said the EHIC "has worked properly in Spain for years'.
"The patient is the one who decides what paperwork to sign, in terms of being treated in Spain," the ministry told the BBC, adding that "the Spanish government will investigate any cases that are presented to it".
A ministry spokeswoman said there was "no proof" for allegations that some British citizens had been pressured, or even tricked, into paying via their private travel insurance.
Mandy Aitchison, editor of the International Travel Insurance Journal, says she believes one of the issues in Spain is the sheer number of people who travel there. More than 10 million British tourists visit Spain every year and about 30 per week need medical treatment.
Ms Aitchison said the way the EHIC is funded "doesn't work particularly well for Spanish hospitals".
"They have ended up employing third-party private companies, who work on their behalf to try and recover the cost of treating lots and lots of foreigners. And obviously in Spain the problem is exacerbated by the number of foreigners they have to treat, because it's a very popular holiday destination," she told the BBC.