The European Health Insurance Card (EHIC) allows any EU citizen to access state medical care when they are travelling in another EU country. In the event of a no-deal Brexit, UK registered EHICs will no longer be valid.
You should have appropriate travel insurance, whether they have an EHIC card or not, as there are limitations to EHIC.
When travelling in the EU and beyond, it is important you take out travel insurance and check that it covers your current circumstances, including any medical conditions. If you have an annual policy, make sure you check the Terms and Conditions and contact your insurance provider if you’re not sure.
For more information please visit - https://www.gov.uk/guidance/uk-nationals-travelling-to-eu-essential-information.