If Spain says you need to renounce your British citizenship then that's what you'll have to do. Even if they take away your passport you will still be a British citizen. You then have the ability to reacquire your British citizenship once per lifetime, though that might cause you to automatically lose your new Spanish citizenship if Spain finds out.

Regarding the process, you would probably have more luck asking on a Spanish language forum. Regarding tax, for UK tax it depends on the deal with the EU. Currently non-UK residents benefit from a UK personal allowance on their UK income if they are EEA citizens, which could change, so if you renounce your British citizenship this could affect you if you live outside the UK and have UK income.

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