Hello, I'm Keith and happy to help you with your question.
Yes, you do. If you are resident in the UK then you are taxed on income world wide. However, if your income from Ireland is taxed at source then under the Double Taxation Treaty between the UK and Ireland any Irish tax deducted is allowable as a tax credit against any UK taxation for the same income stream. The Treaty is designed to ensure that an individual is not taxed in both jurisdictions for the same income. I cannot tell you precicely the tax you will pay unless you tell me exactly what comes in from Ireland. Hazarding a guess, if it is under GBP 1865 quid, then it would be taxed at 20%, 40% over. As a non domicile you could elect to have your Irish income treated on a remittance basis, but under current rules such a procedure is ruinously expensive, 30 to 50K per annum, ouch!
I do hope I have helped you with your question.