From Brits in Spain (British Embassy Facebook site).
We know that some of you are concerned about how you will be able to get the Covid-19 vaccine in Spain – particularly those of you who don’t receive state healthcare.
The Spanish government has been very clear that they will provide the vaccine to everyone in Spain as a matter of public health, regardless of nationality or how you access healthcare in Spain. If you are already registered for state healthcare you will be contacted by your regional health service to make an appointment when it is your turn to be vaccinated.
Because Spain operates its health system regionally, the way people access the vaccine will differ depending on where you live.
We have received the following information from the Spanish regional healthcare authorities for those who are not registered for state healthcare and we continue to seek information for all regions. Please be aware that this is information from the Spanish authorities and is subject to change.
• Valencia Region (Comunidad Valenciana): You will need to go to your local health centre to register. You will be given a provisional health card to cover the vaccination and any other public health needs.