To try to clarify what has been written above:
The E111 was abolished years ago. It has been replaced by the the EHIC.
The Canary Islands are Spanish territory, where the EHIC is valid. (It entitles you to the same free, or reduced -rate, treatment which a Spanish citizen would receive).
The confusion about whether the Canary Islands are within the EU or not comes about because of their special tax status. That means that travellers returning from the Canaries are only allowed the 'non-EU' allowances at British customs but, otherwise, Tenerife is just as 'Spanish' as Madrid is.
Chris