Hello, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
It is normal for pensions to be taxed in the country of origin. The most convenient way is for your State Pension (SP), taxable, but payable gross, to be taxed by the code number on your private pension paid under PAYE being reduced so that at the end of the year your tax position is neutral.
You will, of course, be liable for Spanish taxation on this income, but under the Double Taxation Convention between the UK and Spain the same income stream may only be taxed in one jurisdiction. This is achieved by means of tax credits, the tax deducted in one country being allowed as a tax credit against any liability in the other. Unfortunately, I am aware of the Spanish tax authorities not being very cooperative on this matter and trying to tax twice. You may have to engage a local practitioner in Spain to assist you.
I do hope that you find my reply of assistance.
The fact that the pension income is taxed at source is only half the story. This income is liable to Spanish taxation also less the tax credits if any and she must complete a Spanish tax return unless that authority tells her not to bother.
Thank you for your support.