Hello, I am Keith, one of the experts on Just Answer, and happy to help you with your question.
There is a Double Taxation Treaty between the UK and Portugal which precludes the same income stream being taxed in both jurisdictions. This is achieved by means of tax credits, the tax deducted by one country being allowed as a credit against the tax liabilities in the other. The Treaty does not, however, protect you from differences in rates of taxation.
Will your UK publisher operate PAYE on your behalf or will royalties be paid gross or under a basic rate tax deduction? In the first case you will have no problem. In the second case you will have to register with HMRC as self employed and they will send you a self assessment tax return for completion annually. If you are being paid under deduction of tax at the standard rate then you will have to self assess to recover the overpayment of tax which will result. Finally, of course, you will have to work with the Portugese tax authorities to settle any outstanding tax not covered by your tax credits, if any. You may need local, professional assistance there.
Here is the general comment from AngloInfo:
'All income received by a resident in Portugal, such as salaries, capital gains and real estate income, including income obtained abroad, is taxed in Portugal by the Personal Income Tax (Imposto sobre o Rendimento das Pessoas Singulares, IRS). Note that for income earned abroad, there are several tax treaties that may be applicable to avoid double taxation.'
This web site gives a good background to Portugese Taxation and can be found here:
Having looked at INT400090 it would appear to throw the onus of the tax deduction position on to the royalty payer, but I have given you the consequences of the three possible scenarios.
I do hope that my reply has been of assisttance to you.