The following has been posted by the UK Government:
https://www.gov.uk/foreign-travel-advice/spain/coronavirus#covid-19-vaccines-if-you-live-in-spain
"We have received the following information from certain Spanish regional healthcare authorities for those who are not registered for public healthcare (for example, those who have private health insurance). Please be aware that this is information from the Spanish authorities and is subject to change. Some information may only be available in Spanish.
- Andalusia: You should visit Andalusia’s health service website for details on how to register for the vaccine. More information on the campaign is available on the Andalusia’s vaccine website
- Balearic Islands: You should call 971 211 999 to register for the vaccine. More information is available from the Balearic Islands health service website
- Canary Islands: We are awaiting further information from the Government of the Canary Islands regarding their vaccine plan for those who do not have public healthcare, and will update this section in due course
- Catalonia: You should visit the Catalan regional government website for information on the vaccine programme roll-out in Catalonia and to apply online
- Madrid region: You should call 900 102 112 to register for the vaccine. For more information see the Madrid regional government website
- Murcia: You should register online for the vaccine at the Murcia’s health service website or call 900 121 212
- Valencia region: You should 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.
Details for further regions will be added to this list once available. UK nationals living in Spain who do not live in the areas listed above, should contact their local health centre or private insurance company for more information.
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The Medicines and Healthcare Products Regulatory Agency (MHRA) is the UK authority responsible for assessing the safety, quality and efficacy of vaccines. It has authorised the Pfizer/BioNTech, Oxford/AstraZeneca and Moderna vaccines for temporary supply and use in the UK. Find out more about MHRA approval for these vaccines.
British nationals living overseas should seek medical advice from their local healthcare provider in the country where they reside. Information about vaccines used in other national programmes, including regulatory status, should be available from the local authorities. This list of Stringent Regulatory Authorities recognised by the World Health Organisation may also be a useful source of additional information. Find out more about COVID-19 vaccines on the World Health Organisation COVID-19 vaccines page."
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