Hi,
If you are tax resident in the UK and employed by a UK employer, you are taxable on your employment income in the UK.
If you are tax resident in the UK and receive UK bank interest, then this is taxable in the UK.
As you are dual tax resident, you may find you have to pay taxes in both countries. As the UK is your main place of residence, then the UK has the first rights to tax your sources of UK income. Slovenia may also claim the right to tax them. Article 14 of the double taxation agreement confirms that you are taxable in the UK, however, if you undertake any of that work while in Slovenia, you are taxable on that work in Slovenia.
UNITED KINGDOM / Slovenia DOUBLE TAXATION CONVENTION
Article 23 of the DTA allows you to claim a tax credit in Slovenis against tax paid in the UK.
Thank you.