As I said in the recent post about the FCO & Healthcare information evening (link), there is now a convenio especial for British residents in Spain. This is a pay-in scheme whereby those of working age without health cover of any other sort can buy state insurance for €60 a month The scheme is being run by the Spanish government, and is gradually being rolled out throughout the autonomous regions. All information on its application in the Canaries is available from the Canarian government HERE.
Please note that the system does not provide any rights to subsidised prescriptions, nor to an EHIC, so is neither a cheap nor useful alternative to getting proper healthcare and medical cover in other ways if at all possible. It is also only available to those who are legal residents of over a year’s standing (on a local authority padron as well as a Registro) so is not available for newcomers. This is all I know, so for further information, please click on the Canarian government link above.