As Dzug states, you can apply online for an EHIC, pick up a form at a Post Office, or simply phone up. (I used the phone service. It only takes a minute or two. They just need your name and address plus either your National Insurance number or your National Health number. It's despatched within 5 days).
The web link for the EHIC is here:
http://www.dh.gov.uk/en/Policyandguidance/Heal thadvicefortravellers/index.htm
The phone number is 0845 606 2030.
An EHIC should be regarded as essential for travelling to any EU country (or to Iceland, Liechtenstein, Norway and Switzerland). If you have an accident, or fall ill, you'll receive the same free, or reduced price, treatment that nationals of that country do.
It's important to carry the card with you. If you don't have the card with you at the hospital, you'll be required to pay a bill before you leave. This could cost you many hundreds (or thousands) of pounds. Most insurance companies will not refund such payments because you should have used your EHIC card.
In general, the vast majority of emergency medical expenses within EU countries should be dealt with by presenting your EHIC card. (As stated above, most insurers won't pay out for bills which you wouldn't have received if you'd been carrying the card). The reason for having travel insurance is to cover you for costs which would not be met by the EHIC, like the provision of an air ambulance to bring you home after a medical emergency.
Chris