Ms Aitchison said the way the EHIC is funded "doesn't work particularly well for Spanish hospitals".
BBC: EU warns Spain over hospitals' rejection of EU health card
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.
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.
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