Hello, I am Keith, one of the experts on Just Answer, and pleased to ba able to help you with your question.
Annuities are normally taxed in the country of origin. What should have happened is that the annuity should, after the application of your UK Personal Alowance, been taxed. You would also have had to declare it to the Nigerian Tax authorities. Under the Double Taxation Treaty between the UK and Nigeria the same income stream cannot be taxed in both jurisdictions. This is achieved by means of tax credits, the tax paid in one country being allowed as a tax credit aginst the liability in another. That is what should have happened.
So HMRC did not tax your annuity, but Nigeria did. Therefore the tax paid in Nigeria is allowable as a tax credit against the UK liability, if any. Although these treaties do not protect you against differences in rates of taxation in the end when it all comes out in the wash so to speak it will end up as being an exercise in financial futility.
The letter shows a typical lack of understanding on how taxation and Double Taxation Treaties actually oprate. Your annuity would be taxed in Nigeria irrespective of its taxation in the UK, if any. Depending on the level of the annuity you might have no or minimal exposure to UK taxation anyway.
I do hope that I have been able to shed some light on this murky area for you.