Under many double taxation agreements you may be able to claim exemption from UK tax on ....
This refers to annuities pensions and divîdends and other special types of income that you earn in the UK while working in a DT country, and are normally taxed in the UK.
This does not mean your income that has already been taxed. The whole point of a double taxation agreement is that you are only taxed once, either in the UK or the other country.
In the questioner's case he would not pay tax on his Slovakian income.

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