From experience the most cost effective way around this is to fly back to UK if you need medical treatment. Return flights to UK would be cheaper than a private insurance premium in Tenerife. Weigh up pros & cons, how often are you lkely to need medical treatment? never if lucky. Also do you have enough Spanish to understand what the medical people are telling you without having to pay for a translater. I had to return to UK this year with a medical problem, got immediate flight back to uk, rang doctor from Tenerife and booked appointment for the day I got back and was back in Tenerife in 10 days and it cost me ?150 for return flights, and I had peace of mind that I'd been sorted out.