A small fee (around 9 to 12 euros) is needed to apply either for a NIE or ‘Certificate of Registry as a Resident European Citizen’ at a National Police station. This is paid in advance at any bank of your choice and you take a stamped receipt to the police station with you from the bank along with the rest of your application details.
The tax form is called 790-012 and is a standard form used for paying lots of different taxes/fees for immigration matters, so on the form you need to tick the right box for the service you are paying for.
This form can now only be filled in online and printed out to take to the bank. It is no longer given out at police stations nor immigration offices and cannot be filled in by hand.
The form is very quick to complete and can be filled in by clicking here. (external link). You complete it then press the blue button at the end to get a copy you can print out and sign.
Guidance notes: As the form is in Spanish, below is some advice in English for guidance only (correct at January 2020 and subject to change).
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(We understand that the same form is accepted/used if you carry out these two processes (as a UK citizen) inside an Oficina de Extranjería in your province instead of at a National Police station, but we welcome feedback from you based on your actual experiences if that is not the case so we can help other users).