The Global Health Insurance Card (GHIC) gives you the right to access state-provided healthcare during a temporary stay in the European Union.
The GHIC may not always provide enough cover.
For example, if you are taken to a private clinic in a private ambulance, the GHIC will not cover you.
The GHIC also does not cover the cost of repatriation if you need to be flown back to the UK due to accident or illness.
For these reasons, it's sensible to take out travel insurance as well.