Hi
You would need to review the guidance of the tax treaties between the UK and each of the countries in question.
There is generally an article relating to 'Artistes and Athletes/Sportsmen' please see:
Tax treaties
Where tax is payable in the other countries, then up to 100% of the foreign tax paid can be claimed as a tax credit in a self assessment tax return.
The credit for overseas tax paid, cannot be more than the tax payable in the UK. As your example states he is only able to claim enough to cover the UK tax liability.
Thank you